Class 10-Maths ch-15 Coordinate Geometry

The Line, x = 2 and y = 3 are
(1) parallel to each other
(2) perpendicular to each other
(3) neither parallel nor perpendicular to each other
(4) None of these

The lines, x = -2 and y = 3 intersect at the point _____________.
(1) (- 2, 3)
(2) (2, - 3)
(3) (3, - 2)
(4) (- 3, 2)

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

The centre of a circle is C(2, - 3) and one end of the diameter AB is A(3, 5). Find the coordinates of the other end B.
(1) (1, - 11)
(2) (5, 2)
(3) (1, 8)
(4) (1, 11)

The angle made by the line $\sqrt{3 x} - y + 3 = 0$ with the positive direction of X-axis is ______________.
(1) $30 °$
(2) $45 °$
(3) $60 °$
(4) $90 °$

The point on X-axis which are at a distance of $\sqrt{13} u n i t f r o m (- 2, 3) i s________________.$
(1) $(0, 0), (- 2, - 3)$
(2) $(0, 0), (- 4, 0)$
(3) $(0, 0), (2, 3)$
(4) $(0, 0), (4, 0)$

The point P lying in the fourth quadrant which is at a distance of 4 units form X-axis and 3 units from Y-axis is_____________.
(1) (4, - 3)
(2) (4, 3)
(3) (3, - 4)
(4) (- 3, 4)

The radius of a circle with centre (- 2, 3) is 5 units. The point (2, 5) lies
(1) on the circle
(2) inside the circle
(3) outside the circle
(4) None of these

The points (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 these

10.

$F i n d λ, i f t h e l i n e 3 x - λ y + 6 = 0 p a s s e s t h r o u g h t h e p o i n t (- 3, 4) .$
(1) $\frac{3}{4}$
(2) $\frac{- 3}{4}$
(3) $\frac{4}{3}$
(4) $\frac{- 4}{3}$

11.

If A(-2, 3) and B(2, 3) are two vertices of $∆ A B C$ and G(0, 0) is its centroid, then the coordinates of C are__________.
(1) (0, - 6)
(2) (- 4, 0)
(3) (4, 0)
(4) (0, 6)

12.

$L e t ∆ A B C b e a r i g h t t r i a n g l e i n w h i c h A (0, 2) a n d B (2, 0) . T h e n t h e c o o r d i n a t e s o f C c a n b e__________.$
(1) (0,0)
(2) (0, 2)
(3) Either (1) or (2)
(4) None of these

13.

If A(4, 7), B(2, 5), C(1, 3) and D(- 1, 1) are the four points, then the lines AC and BD are ____________.
(1) perpendicular to each other
(2) parallel to each other
(3) neither parallel nor perpendicular to each other
(4) none of these

14.

Find the area of the triangle formed by the line 5x - 3y + 15 = 0 with coordinate axes.
(1) 15 $c m^{2}$
(2) 5 $c m^{2}$
(3) 8 $c m^{2}$
(4) $\frac{15}{2} c m^{2}$

15.

Equation of a line whose inclination is $45 °$ and making an intercept of 3 units on X-axis is.
(1) x + y - 3 = 0
(2) x - y - 3 = 0
(3) x - y + 3 = 0
(4) x + y + 3 = 0

16.

The centre of a circle is C(2, k). If A(2, 1) and B(5, 2) are two points on its circumference, then the value of k is _______________.
(1) 6
(2) 2
(3) - 6
(4) - 2

17.

The lines x = - 1 and y = 4 are __________.
(1) perpendicular to each other
(2) parallel to each other
(3) neither parallel nor perpendicular to each other
(4) none of these

18.

The distance between the points (2k + 4, 5k) and (2k, - 3 + 5k) in units is_________________.
(1) 1
(2) 2
(3) 4
(4) 5

19.

The equation of the line with inclination $45 °$ and passing through the point ( -1, 2) is ___________.
(1) x + y + 3 = 0
(2) x - y + 3 = 0
(3) x - y - 3 = 0
(4) x + y - 3 = 0

20.

The distance between the point (3k + 1, -3k) and (3k - 2, -4 - 3k) (in units) is ___________.
(1) 3k
(2) 5k
(3) 5
(4) 3

21.

The angle made by the line $x - \sqrt{3} y + 1 = 0$ with the positive Y-axis is _____________.
(1) $60 °$
(2) $30 °$
(3) $45 °$
(4) $90 °$

22.

If $∆ A B C$ is a right triangle in which A(3, 0) and B(0, 5), then the coordinates of C can be _______________.
(1) (5, 3)
(2) (3, 5)
(3) (0, 0)
(4) Both (2) and (3)

23.

If the roots of the quadratic equation $2 x^{2} - 5 x + 2 = 0$ are the intercepts made by a line on the coordinate axes, then the equation of the line can be
(1) 4x + y = 2
(2) 2x + 5y + 2
(3) x + 4y = 2
(4) Both (1) and (3)

24.

The inclination of the line $\sqrt{3} x - y + 5 = 0$ with X-axis is ____________.
(1) $90 °$
(2) $45 °$
(3) $60 °$
(4) $30 °$

25.

The equation of the line parallel to 3x-2y+7 = 0 and making an intercept $- 4$ on X-axis is
(1) 3x-2y+12 = 0
(2) 3x-2y-12 = 0
(3) 3x+2y-12 = 0
(4) 3x+2y+12 = 0

26.

A triangle is formed by the lines x+y = 8, X-axis and Y-axis. Find its centroid.
(1) $(\frac{8}{3}, \frac{8}{3})$
(2) (8, 8)
(3) (4, 4)
(4) (0, 0)

27.

The point which divides the line joining the points A(1,2) and B(-1, 1) internally in the ratio 1 : 2 is ____________.
(1) $(\frac{- 1}{3}, \frac{5}{3})$
(2) $(\frac{1}{3}, \frac{5}{3})$
(3) $(- 1, 5)$
(4) (1, 5)

28.

Find the area of the triangle formed by the line 3x-4y+12 = 0 with the coordinate axes.
(1) 6 $u n i t s^{2}$
(2) 12 $u n i t s^{2}$
(3) 1 $u n i t s^{2}$
(4) 36 $u n i t s^{2}$

29.

The equation of a line whose sum of intercepts is 5 and the area of the triangle formed by the line with positive coordinate axis is 2 sq. units can be
(1) x + y = 4
(2) x + 4y = 4
(3) y + 4x + 4 = 0
(4) y = x + 4

30.

Find the equation of a line which divides the line segment joining the points (1, 1) And (2, 3) in the ratio 2 : 3 perpendicularly.
(1) 5x - 5y + 2 = 0
(2) 5x + 5y + 2 = 0
(3) x - 2y - 5 = 0
(4) x + 2y + 7 = 0

31.

The equation of the line making an angle of $45 °$ with X-axis in positive direction and having Y-intercept as $- 3$ is _______________.
(1) 3x-y+1 = 0
(2) 3x+y-1 = 0
(3) x-y+3 = 0
(4) x-y = 3

32.

The ratio in which the line joining points (a+b, b+a) and (a-b, b-a) is divided by the point (a, b) is _________.
(1) b : a internally
(2) 1 : 1 internally
(3) a : b externally
(4) 2 : 1 externally

33.

Which of the following lines is perpendicular to x + 2y + 3 = 0?
(1) $\sqrt[2]{2} x - y + 3 = 0$
(2) $\sqrt{2} x + \sqrt{2} y - 5 = 0$
(3) $\sqrt[2]{2} x - \sqrt{2} y + 3 = 0$
(4) $x + \sqrt{2} y + 4 = 0$

34.

The equation of the line passing through the point of intersection of the lines x+2y+3 = 0 and 2x - y + 5 = 0 and parallel to X-axis is ___________.
(1) 5y+1 = 0
(2) 5x - 13 = 0
(3) 5x + 13 = 0
(4) 5y - 1 = 0

35.

Find the equation of a line which divides the line segment joining the points (1, -2) and (3, -1) in the ratio 3 : 1 perpendicularly.
(1) x - 2y - 5 = 0
(2) 6x + 4y - 5 = 0
(3) 3x + 2y - 5 = 0
(4) 8x + 4y - 15 = 0

36.

If x + p = 0, y + 4 = 0 and x +2y + 4 = 0 are concurrent, then p = __________.
(1) 4
(2) - 2
(3) - 4
(4) 2

37.

The perpendicular bisector of the side PQ is

(1) x - y = 0
(2) x + y - 2 = 0
(3) 3x - 2y - 2 = 0
(4) x + 2y - 6 = 0

38.

The ortho-centre of the triangle formed by the vertices A(4, 6), B(4, 3) and C(2, 3) is ______________.
(1) (2, 3)
(2) (4, 3)
(3) (4, 6)
(4) (3, 4)

39.

The circum-centre and the ortho-centre of the triangle formed by the sides y = 0, x = 0 and 2x + 3y = 6 are respectively____________.
(1) (3, 2), (0, 0)
(2) $(\frac{3}{2}, 1), (0, 0)$
(3) (-3, 1), (0,0)
(4) $(\frac{- 3}{2}, 1), (0, 0)$

40.

The equation of median drawn to the side BC of $∆ A B C$ whose vertices are A(1, -2), B(3, 6) and C(5, 0) is ___________.
(1) 5x - 3y -11 = 0
(2) 5x + 3y - 11 = 0
(3) 3x - 5y + 11 = 0
(4) 3x - 5y - 11 = 0

41.

Find the equation of the line passing through (1, 1) and forming an area of 2 sq. units with positive coordinate axis.
(1) 2x + 3y = 5
(2) x - y + 2 = 0
(3) x + y - 2 = 0
(4) x - y + 1 = 0

42.

If the vertices of a triangle are A(3, -3), B(-3, 3) and C $(- \sqrt[3]{3}, - \sqrt[3]{3})$ , then the distance between the ortho-centre and the circum-centre is ______________.
(1) $\sqrt[6]{2} u n i t s$
(2) $\sqrt[6]{3} u n i t s$
(3) 0 unit
(4) None of these

43.

The circum-centre of the triangle formed by the lines x + 4y = 7, 5x + 3y = 1 and 3x - 5y = 21 is _____________.
(1) (-3, 2)
(2) (3, 1)
(3) (3, -1)
(4) (-3, -2)

44.

If the line (3x - 8y + 5) + a(5x - 3y + 10) = 0 is parallel to X-axis, then a is___________.
(1) $- \frac{8}{3}$
(2) $- \frac{3}{5}$
(3) - 2
(4) $- \frac{1}{2}$

45.

Find the equation of the median of the triangle, formed by the line 8x+5y = 40 with the coordinate axes. Given that the median is passing through the origin.
(1) 5x - 8y = 0
(2) 5x + 8y = 0
(3) 8x - 5y = 0
(4) 8x + 5y = 0

46.

Find the area of a triangle formed by the llines 4x-y-8 = 0, 2x+y-10 = 0 and y = 0 (in sq. units).
(1) 5
(2) 6
(3) 4
(4) 3

47.

Find the length of the longest side of the triangle formed by the lline 3x+4y = 12 with the coordinate axes.
(1) 9
(2) 16
(3) 5
(4) 7

48.

The following are the steps involved in finding the area of the triangle with vertices (2, 3), (4, 7) and (8, 5). Arrange them in the sequential order from first to last.
$(A) \frac{1}{2} |(- 2) 2 - (- 4) (- 4)| = \frac{1}{2} |- 2| = 10 s q . u n i t s (B) A r e a o f t r i a n g l e = \frac{1}{2} |\begin{matrix} x_{1} - x_{2} & x_{2} - x_{3} \\ y_{1} - y_{2} & y_{2} - y_{3} \end{matrix}| (C) L e t (x_{1}, y_{1}) = (2, 3), (x_{2}, y_{2}) = (4, 7) a n d (x_{3}, y_{3}) = (8, 5) (D) A r e a o f t r i a n g l e = \frac{1}{2} |\begin{matrix} 2 - 4 & 4 - 8 \\ 3 - 7 & 7 - 5 \end{matrix}|$

(1) ABCD
(2) CBDA
(3) CBAD
(4) None of these

49.

The following are the steps involved in finding the centroid of the triangle with vertices (5, 4), (6, 7) and (1, 1). Arrange them in sequential order from first to last.
$(A) T h e r e q u i r e d c e n t r o i d (4, 4) (B) T h e c e n t r o i d o f t h e t r i a n g l e w i t h t h e v e r t i c e s (x_{1}, y_{1}), (x_{2}, y_{2}) a n d (x_{3}, y_{3}) i s (\frac{x_{1} + x_{2} + x_{3}}{3}, \frac{y_{1} + y_{2} + y_{3}}{3}) (C) T h e c e n t r o i d i s (\frac{5 + 6 + 1}{3}, \frac{4 + 7 + 1}{3})$

(1) ABC
(2) CBA
(3) BAC
(4) BCA

50.

In what ratio does the line 4x+3y-13 = 0 divide the line segment joining the points (2, 1) and (1, 4) ?
(1) 3 : 2 internally
(2) 2 : 3 externally
(3) 2 : 3 internally
(4) 3 : 2 externally

51.

If A(3, 4), B(1, -2) are the two vertices of triangle ABC and G(3, 5) is the centroid of the triangle, then the equation of AC is ______________.
(1) 4x-5y-7 = 0
(2) 4x-5y+8 = 0
(3) 9x-2y-23 = 0
(4) 9x-2y-19 = 0

52.

If ax+4y+3 = 0, bx+5y+3 = 0 and cx+6y+3 = 0 are concurrent lines, then a + c = __________.
(1) 3b
(2) 2b
(3) b
(4) 4b

53.

If (5, 3), (4, 2) and (1, -2) are the mid points of sides of triangle ABC, then the area of $∆ A B C$ is
(1) 2 sq. units
(2) 3 sq. units
(3) 1 sq. unit
(4) 4 sq. units

54.

Area of the region formed by $4 |x| + 3 |y| = 12$ is _____________.
(1) 18 sq. units
(2) 20 sq. units
(3) 24 sq. units
(4) 36 sq. units

55.

Find the radius of the circle which passes through the origin, (0, 4) and (4, 0).
(1) 2
(2) $\sqrt[4]{2}$
(3) $\sqrt{8}$
(4) $\sqrt[3]{2}$

56.

Find the circum-centre of the triangle whose vertices are (0, 0), (3, $\sqrt{3}$ ), (0, $\sqrt[2]{3}$ ).
(1) $(1, \sqrt{3})$
(2) $(\sqrt{3}, \sqrt{3})$
(3) $(\sqrt[2]{3}, 1)$
(4) $(2, \sqrt{3})$

57.

Find the ortho-centre of the triangle formed by the lines 3x-4y = 10, 8x+6y = 15 and Y-axis.
(1) $(\frac{3}{5}, \frac{7}{5})$
(2) $(\frac{12}{5}, \frac{- 7}{10})$
(3) $(\frac{3}{5}, \frac{12}{5})$
(4) $(\frac{12}{5}, \frac{- 3}{10})$

58.

The equation of a line which passes through (2, 3) and the product of whose intercepts on the coordinate axis is 27, can be ____________.
(1) 5x+4y = 22
(2) $3 x - y = 3$
(3) 3x+4y = 18
(4) 2x+3y = 13

59.

Which of the following points belongs to the region indicated by the inequation 2x + 3y < - 6?

(1) (0, 2)
(2) (-3, 8)
(3) (3, -2)
(4) (-2, -2)

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