Class 9 Pearson - Coordinate GeometryContact Number: 9667591930 / 8527521718

Page:

1.

If (1, –3), (–2, –3) and (–2, 2) are the three vertices of a parallelogram taken in the order, then the fourth vertex is ____________.?

(1) (–1, –2)

(2) (1, 2)

(3) (–1, 2)

(4) (1, –2)

2.

Find the equation of the line that passes through point (5, –3) and makes an intercept 4 on the *X*-axis.

(1) 3*x* – *y* + 12 = 0

(2) 3*x* + *y* + 12 = 0

(3) 3*x* – *y* – 12 = 0

(4) 3*x* + *y* – 12 = 0

3.

The inclination of line $x-\sqrt{3y}+1=0$ with the positive *X*–axis is ____________.

(1) 60°

(2) 30°

(3) 45°

(4) 90°

4.

The equation of the line perpendicular to *Y*-axis and passing through point (–5, 7) is ____________.

(1) *y* = –5

(2) *x* = 7

(3) *x* = –5

(4) *y* = 7

5.

If (2, 0) and (–2, 0) are the two vertices of an equilateral triangle, then the third vertex can be __________.

(1) (0, 0)

(2) (2, –2)

(3) $(0,2\sqrt{3})$

(4) $(\sqrt{3},\sqrt{3})$

6.

The point (*a*, *b* + *c*), (*b*, * c* + *a*) and (*c*, * a* + *b*)

(1) are collinear.

(2) form a scalene triangle.

(3) form an equilateral triangle.

(4) None of the above

7.

The equation of the line making equal intercepts and passing through the point (–1, 4) is ____________. ?

(1) *x* – *y* = 3

(2) *x* + *y *+ 3 = 0

(3) *x* + *y* = 3

(4) *x* – *y *+ 3 = 0

8.

The endpoint of the longest chord of a circle are (– 4, 2) and (– 6, –8). Find its centre.

(1) $(-\frac{10}{3},-2)$

(2) (–5, –2)

(3) (–5, –4)

(4) (–5, –3)

9.

The equation of the line passing through point (–3, –7) and making an intercept of 10 units on *X*-axis can be _________.

(1) 4*x* + 3*y* = –9

(2) 8*x* – 3*y* = 80

(3) 7*x* – 13*y *– 70 = 0

(4) 7*x* + 13*y *– 70 = 0

10.

The point on the *Y*-axis which are at a distance of 5 units from (4, –1) are __________.

(1) (0, –2), (0, 4)

(2) (0, 2), (0, –4)

(3) (0, 2), (0, 4)

(4) (0, –2), (0, –4)

11.

If the slope and the *y*-intercept of a line are the roots of the equation *x*^{2} – 7*y* – 18 = 0, then the equation of the line can be ________.

(1) 2*x* + *y *– 9 = 0

(2) 2*x* – *y *+ 9 = 0

(3) 9*x* + *y *+ 2 = 0

(4) 9*x* + 2*y *– 2 = 0

12.

If the points (*k*, *k* – 1), (*k* + 2, *k* + 1) and (*k*, *k* +3) are three consecutive vertices of a square, then its area (in square units) is ___________.

(1) 2

(2) 4

(3) 8

(4) 6

13.

The equation of the line making intercepts of equal magnitude and opposite signs, and passing through the point (– 3, –5) is __________.

(1) *x* – *y *= 2

(2) 2*x* + *y *= – 4

(3) 3*x* + 3*y *= 6

(4) *x* – *y * = –10

14.

If the endpoint of the diameter of a circle are (–2, 3) and (6, –3), then the area of the circle (in square units) is __________.

(1) $\frac{550}{3}$

(2) $\frac{540}{7}$

(3) $\frac{560}{7}$

(4) $\frac{550}{7}$

15.

The inclination of the line $\sqrt{3x}-y+3=0$ with the positive *X*-axis is ________.

(1) 30°

(2) 45°

(3) 60°

(4) 90°

16.

The two lines 3*x* + 4*y* – 6 = 0 and 6*x* + *ky* – 7 = 0 are such that any line which is perpendicular to the first line is also perpendicular to the second line. Then, *k* = _________.

(1) –8

(2) –6

(3) 6

(4) 8

17.

The line *x* = *my*, where *m* < 0, lies in the quadrants.

(1) 1st, 2nd

(2) 2nd, 4th

(3) 3rd, 4th

(4) 3rd, 1st

18.

Find the area in square units, of the rhombus with vertices (2, 1), (–5, 2), (–4, –5) and (3, –6), taken in that order.

(1) 24

(2) 48

(3) 36

(4) 50

19.

The radius of a circle with centre (–2, 3) is 5 units, then the point (2, 5) lies ________.

(1) on the circle

(2) inside the circle

(3) outside the circle

(4) none of the above

20.

One end of the diameter of a circle with the centre as origin is (–2, 10). Find the other end of the diameter.

(1) (–2, –10)

(2) (0, 0)

(3) (2, –10)

(4) (2, 10)

21.

If the roots of the quadratic equation *x*^{2} – 7*x* + 12 = 0 are intercepts of a line, then the equation of the line can be ________.

(1) 2*x* + 3*y* = 6

(2) 4*x* + 3*y* = 12

(3) 4*x* + 3*y* = 6

(4) 3*x* + 4*y* = 6

22.

Find the value of λ, if the line *x* – 3*y* + 4 + λ(8*x* – 3*y* + 2) = 0 is parallel to the *X*-axis.

(1) $\frac{1}{5}$

(2) $\frac{5}{8}$

(3) $-\frac{3}{8}$

(4) $-\frac{1}{8}$

23.

The slope of the line joining the points (2, *k* – 3) and (4, –7) is 3. Find *k*.

(1) –10

(2) –6

(3) –2

(4) 10

24.

The angle between the lines *x* = 10 and *y *= 10 is _________.

(1) 0°

(2) 90°

(3) 180°

(4) none of these

25.

The two lines 5*x* + 3*y* + 7 = 0 and *kx* – 4*y *+ 3 = 0 are perpendicular to the same line. Find the value of *k*.

(1) $-\frac{20}{7}$

(2) $-\frac{20}{3}$

(3) $\frac{20}{9}$

(4) $\frac{12}{5}$

26.

The lines *x* – 2*y* + 3 = 0, 3*x* – *y *= 1 and *kx* – *y *+ 1 = 0 are concurrent.. Find *k*.

(1) 1

(2) $\frac{1}{2}$

(3) $\frac{3}{2}$

(4) $\frac{5}{2}$

27.

Find the quadrant in which the lines 2*x* + 3*y* – 1 = 0 and 3*x* + *y* – 5 = 0 intersect each other.

(1) 1st quadrant

(2) 2nd quadrant

(3) 3rd quadrant

(4) 4th quadrant

28.

The circum-centre of the triangle formed by points *O*(0, 0), *A*(6, 0), and *B*(0, 6) is ______.

(1) (3, 3)

(2) (2, 2)

(3) (1, 1)

(4) (0, 0)

29.

The lines 3*x* – *y* + 2 = 0 and *x* + 3*y* + 4 = 0 intersect each other in the _______.

(1) 1st quadrant

(2) 4th quadrant

(3) 3rd quadrant

(4) 2nd quadrant

30.

Centre of the circle is (*a*, *b*). If (0, 3) and (2, 0) are two points on ac circle, then find the relation between *a* and *b*.

(1) 4*a* – 6*b* – 5 = 0

(2) 4*a* + 6*b* – 5 = 0

(3) – 4*a* + 5 = 0

(4) 4*a* – 6*b* + 5 = 0

31.

The equation of a line passing through *P*(3, 4), such that *P* bisects the part of it intercepted between the coordinate axes is ____________?

(1) 3*x* + 4*y* = 25

(2) 4*x* + 3*y* = 24

(3) *x* – *y* = –1

(4) *x* + *y* = 7

32.

The line 7*x* + 4*y* = 28 cuts the coordinate axes at *A* and *B*. If *O* is the origin, then the ortho-centre of Δ*OAB* is ____________.

(1) (4, 0)

(2) (0, 7)

(3) (0, 0)

(4) None of these

33.

If the roots of the quadratic equation *x*^{2} – 5*x* + 6 = 0 are the intercepts of a line, then the equation of the line can be ____________.

(1) 2*x* + 3*y* = 6

(2) 3*x* + 2*y* = 6

(3) Either (1) or (2)

(4) None of these

34.

The equation of the line whose *x*-intercept is 5, and which s parallel to the line joining the points (3, 2) and (–4, –1) is ____________.

(1) 4*x* + 7*y* – 20 = 0

(2) 3*x* – 7*y* + 3 = 0

(3) 3*x* + 2*y* + 15 = 0

(4) 3*x* – 7*y* – 15 = 0

35.

Find the area of the triangle formed by the line 3*x* – 4*y* + 12 = 0 with the coordinate axes.

(1) 6 units^{2}

(2) 12 units^{2}

(3) 1 units^{2}

(4) 36 units^{2}

36.

The joining the points (2*m *+ 2, 2*m*) and (2*m* + 1, 3) passes through (*m* + 1, 1), if the values of *m* are _________.

(1) $5,-\frac{1}{5}$

(2) 1, –1

(3) $2,-\frac{1}{2}$

(4) $3,-\frac{1}{3}$

37.

The length (in units) of the line joining the points (4, 3) and (–4, 9) intercepted between the coordinate axes is ____________.

(1) 10

(2) 8

(3) 6

(4) 4

38.

The equation of a line parallel to 8*x* – 3*y* + 15 = 0 and passing through the point (–1, 4) is ____________.

(1) 8*x* – 3*y* – 4 = 0

(2) 8*x* – 3*y* – 20 = 0

(3) 8*x* – 3*y* + 4 = 0

(4) 8*x* – 3*y* + 20 = 0

39.

(0, 0), $(3,\sqrt{3})$ and $(0,2\sqrt{3})$ are the three vertices of a triangle. The distance between the orthocentre and the cirum-centre of the triangle is _________. (in units)

(1) $\sqrt{3}$

(2) $\sqrt{5}$

(3) $\sqrt{6}$

(4) 0

40.

In a parallelogram *PQRS*, *P*(15, 9), *Q* (7, 10), *R*(–5, –4), then the fourth vertex *S* is __________.

(1) (3, –2)

(2) (3, –4)

(3) (9, –5)

(4) (3, –5)

41.

If the roots of the quadratic equation 3*x*^{2} – 2*x* – 1 = 0, are the intercepts of a line, then the line can be ________.

(1) *x* – 3*y *– 1 = 0

(2) 3*x* – *y *+ 1 = 0

(3) Either (1) or (2)

(4) None of these

42.

The length (in units) of a line segment intercepted between the coordinate axes by the line joining the points (1, 2) and (3, 4) is ___________.

(1) 4

(2) 6

(3) 8

(4) $\sqrt{2}$

43.

If *A* = (3, –4), *B* = (7, 0) and *C* = (14, –7) are the three consecutive vertices of a parallelogram *ABCD*, then find the slope of the diagonal *BD*. The following are the steps involved in solving the above problem. Arrange them in sequential order.

(A) $(\frac{x+7}{2},\frac{y+0}{2})=(\frac{3+14}{2},\frac{-4-7}{2})$

(B) The slope of $BD=\frac{-11-0}{10-7}=\frac{-11}{3}$.

(C) $\frac{x+7}{2}=\frac{17}{2}$ and $\frac{y+0}{2}=\frac{-11}{2}$

⇒ *x* = 10, *y* = – 11

∴ D = (10, – 11).

(D) Let the fourth vertex by *D*(*x*, *y*). We know that the diagonals of a parallelogram bisect each other.

(1) ADCB

(2) DCAB

(3) DACB

(4) CDAB

44.

If *A* = (1, –6), *B* = (5, –2) and *C* = (12, –9) are the three consecutive vertices of a parallelogram, then find the fourth vertex. The following are the steps involved in solving the above problem. Arrange them in sequential order from beginning to end.

(A) $\frac{5+x}{2}=\frac{13}{2},\frac{-2+y}{2}=\frac{-15}{2}\Rightarrow x=8$, and *y* = – 13. Therefore, D = (8, –13).

(B) $\therefore (\frac{5+x}{2},\frac{-2+y}{2})=(\frac{1+12}{2},\frac{-6-9}{2})$.

(C) Let the fourth vertex be *D* = (*x*, *y*).

(D) We know that diagonals of a parallelogram bisect each other.

(1) ACBD

(2) ABDC

(3) CBDA

(4) CDBA

45.

Find the product of intercepts made by the line 7*x* – 2*y* – 14 = 0 with coordinate axes.

(1) – 7

(2) 2

(3) 14

(4) – 14

46.

Find the value of *k*, if points (–2, 5), (–5, –10) and (*k*, –13) are collinear.

(1) $\frac{5}{28}$

(2) $\frac{-28}{5}$

(3) 28

(4) 5

47.

The inclination of the line $\sqrt{3y}-x+24=0$, is _______.

(1) 60°

(2) 30°

(3) 45°

(4) 135°

48.

Find the product of intercepts of the line 3*x* + 8*y* – 24 = 0.

(1) 8

(2) 24

(3) 3

(4) 12

49.

Find the value of *k*, if points (10, 14), (–3, 3) and (*k*, –8) are collinear.

(1) 16

(2) 18

(3) – 18

(4) – 16

50.

The inclination of the line *y* – *x* + 11 = 0, is ________.

(1) 30°

(2) 60°

(3) 0°

(4) 45°

51.

The equation of a line whose *x*-intercept is – 3 and which is parallel to 5*x* + 8*y* – 7 = 0 is ________.

(1) 5*x* + 8*y* + 15 = 0

(2) 5*x* + 8*y* – 15 = 0

(3) 5*x* + 8*y* – 17 = 0

(4) 5*x* – 8*y* – 18 = 0

52.

The equation of the line perpendicular to the line inclined equally to the coordinate axes and passing through (2, –3) is _____________.

(1) *x* + *y* + 1 = 0

(2) *x* – *y* – 2 = 0

(3) *x* + *y* + 2 = 0

(4) 2*x* + *y* – 1 = 0

53.

A triangle is formed by point (6, 0), (0, 0) and (0, 6). How many points with the integer coordinates are in the interior of the triangle?

(1) 7

(2) 6

(3) 8

(4) 10

54.

The equation of one of the diagonals of a square is 3*x* – 8*y* + 4 = 0. Find the equation of the other diagonal passing through the vertex (4, –6).

(1) 8*x* + 3*y* – 15 = 0

(2) 3*x* – 8*y* – 11 = 0

(3) 8*x* + 3*y* – 14 = 0

(4) 8*x* + 3*y* + 15 = 0

55.

The line 2*x *+ 3*y* – 6 = 0 and 2*x *+ 3*y* – 12 = 0 are represented on the graph. The difference between the areas of triangles formed by the lines with the coordinate axes is _______. (in sq. units)

(1) 12

(2) 9

(3) 6

(4) 3

56.

The equation of a line whose *x*-intercept is 11 and perpendicular to 3*x *– 8*y* + 4 = 0, is _________.

(1) 7*x* + 3*y* – 77 = 0

(2) 8*x* + 3*y* – 88 = 0

(3) 5*x* + 3*y* – 55 = 0

(4) 3*x* + 8*y* – 88 = 0

57.

*A*(–11, 7) and *B*(–10, 6) are the points of trisection of a line segment *PQ*. Find the coordinates of *P* and *Q*.

(1) (–12, 8); (–9, 5)

(2) (–12, –8); (–9, 5)

(3) (12, 0); (9, –5)

(4) (12, –8); (9, –5)

58.

If one of the diagonals of a rhombus is 3*x* – 4*y* + 10 = 0, then find the equation of the other diagonal which passes through point (–2, –3).

(1) 4*x* + 3*y* + 17 = 0

(2) 3*x* – 4*y* + 15 = 0

(3) 4*x* + 3*y* – 15 = 0

(4) 3*x* – 4*y* – 11 = 0

59.

The equation of the diagonal *AC* of a square *ABCD* is 3*x* + 4*y* + 12 = 0. Find the equation of *BD*, where *D* is (2, –3)

(1) 4*x* – 3*y* – 8 = 0

(2) 4*x* – 3*y* – 17 = 0

(3) 4*x* – 3*y* + 17 = 0

(4) 4*x* + 3*y* – 17 = 0

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