Find the coordinates of the points which divide the line segment joining A(–2, –2) and B(2, 8) into four equal parts.
Find the lengths of the medians of the triangle whose vertices are (5, 6), (3, 8) and (–1, 2).
The points A, B and C are collinear and AB = BC. If the coordinates of A, B and Care (3, a), (1, 3) and (b, 4) respectively, then find the values of a and b. CBSE 2013
Find the coordinates of the point Q on the X-axis, which lies on the perpendicular bisector of the line segment joining the points A(–5, –2) and B (4, –2). Name the type of triangle formed by the points Q, A and B. NCERT Exemplar
Two vertices of a triangle are (8, –6) and (–4, 6). The area of the triangle is 120 sq. units. Find the third vertex if it lies on x – 2y = 6.
If centroid of triangle is (3, –5) and two vertices of triangle are (4, –8) and (3, 6), then find the third vertex.
In a ∆ABC, the coordinates of points A, B and C are (3, 2), (6, 4) and (9, 3), respectively. Find the coordinates of centroid G. Also, find the areas of ∆ABG and ∆ACD. CBSE 2013
If the points A (1, –2), B (2, 3), C(–3, 2) and D(–4, –3) are the vertices of a parallelogram ABCD, then taking AB as the base, find the height of this parallelogram. CBSE 2013
Find the area of a parallelogram ABCD, if three of its vertices are A(2, 4), B(2 + *, 5) and C(2, 6). CBSE 2013
Find the perpendicular distance of A (5, 12) from the Y-axis.
If A is a point on Y-axis, whose ordinate is 3 and coordinates of point B is (‒5, 2), then find the distance AB.
If is the mid-point of the line segment joining the points (K, 0) and , then find the value of k. CBSE 2015
Find the radius of the circle whose end points of diameter are (24, 1) and (2, 23). CBSE 2015
What is the distance between the points and ?
Find the point which lies on the perpendicular bisector of the line segment joining the points A(‒2, ‒5) and B (2, 5). NCERT Exemplar
Find the area of triangle with vertices (a, b + c), (b, c + a) and (c, a + b). NCERT Exemplar
AOBC is a rectangle whose three vertices are A (0, 3), O (0, 0) and B (5, 0). What are the length of its diagonals? NCERT Exemplar
Find the perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0). NCERT Exemplar
[Hint The perimeter of a triangle is the sum of lengths of its three sides, so first find the length of the three sides and then add them.]
If the point P (2, 1) lies on the line segment joining the points A (4, 2) and B (8, 4), then find the relation between AP and AB. NCERT Exemplar
If the point C(K, 4) divides the join of points A(2, 6) and B(5, 1) in the ratio 2 : 3, find the value of k?
In the following figure, find the area of ΔABC. CBSE 2013
If the centroid of triangle formed by points P (a, b), Q (b, c) and R (c, a) is at the origin. What is the value of (a + b + c)?
Prove that the points (3, 0), (6, 4) and (‒1, 3) are the vertices of a right angled isosceles triangle. CBSE 2016
Check, whether the points (‒4, 0), (4, 0) and (0, 3) are the vertices of an isosceles triangle or equilateral triangle. NCERT Exemplar, CBSE 2014
If the points A (4, 3) and B (x, 5) are on the circle with center O (2, 3), then find the value of x2 + 5.
Show that if a circle has its centre at the origin and a point P(5, 0) lies on it, then the point Q (6, 8) lies outside the circle. NCERT Exemplar
Point P divides the line segment joining the points A (‒1, 3) and B (9, 8) such that . If P lies on the line x ‒ y + 2 = 0, then find the value of k. CBSE 2010
Show that the points A (‒ 6, 10), B (‒ 4, 6) and C (3, ‒ 8) are collinear, such that . NCERT Exemplar
If the points (P, q), (M, n) and (P ‒ M, q ‒ n) are collinear. Show that Pn = qM. CBSE 2010
Prove that the area of triangle whose vertices are (t, t ‒ 2), (t + 2, t + 2) and (t + 3, t), is independent of t.
Show that ΔABC with vertices A (‒ 2, 0), B (0, 2) and C (2, 0) is similar to ΔDFE with vertices D (‒ 4, 0), E (4, 0) and F (0, 4). NCERT Exemplar
If the point A (2, ‒ 4) is equidistant from P (3, 8) and Q (‒ 10, y), then find the value of y. Also, find distance PQ. NCERT Exemplar
Show that quadrilateral PQRS formed by vertices P (22, 5), Q (7, 10), R (12, 11) and S (3, 24) is not a parallelogram. CBSE 2015
ABCD is a rectangle formed by the points A (‒1, ‒1), B (‒1, 4), C (5, 4) and D (5, ‒1). P, Q, R and S are the mid-points of AB, BC, CD, and DA, respectively. Is the quadrilateral PQRS a square, a rectangle or a rhombus? Justify your answer.
If the area of ΔABC formed by A(x, y), B(1, 2) and C(2, 1) is 6 sq units, then prove that x + y = 15 or x + y + 9 = 0. CBSE 2013
In the given figure, in ΔABC, D and E are the mid-points of the sides BC and AC respectively. Find the length of DE. Prove that . CBSE 2011
Find the area of parallelogram ABCD, if three of its vertices are A(2, 4), B and C (2, 6). CBSE 2013
If a ≠ b ≠ c, then prove that the points (a, a2), (b, b2) and (c, c2) can never be collinear.
Four points A (6, 3), B (‒3, 5) C (4, ‒2) and D (x, 3x) are given such that , find x.
The vertices of a ΔABC are A (7, 8), B (4, 2) and C (8, 2). The mid-point of the side BC is (6, 2). Show that the median AD divides the ΔABC into two triangles equal in area. Also, find the area of ΔABC to verify your answer. CBSE 2015
The vertices of ΔABC are A (‒2, 0), B (2, 0) and C (0, 2) and that of ΔPQR are P (‒4, 0), Q (4, 0) and R (0, 4). Verify that the ratio of the areas of the two triangles is equal to the square of the ratio of their corresponding sides. CBSE 2015
A (6, 1), B (8, 2) and C (9, 4) are three vertices of a parallelogram ABCD. If E is the mid-point of DC, then find the area of ΔADE. NCERT Exemplar
The coordinates of A, B, C are (7, 4), (‒2, 6) and (5, ‒1), respectively and P is any point (x, y). Show that the ratio of the areas of ΔPBC and ΔABC is .
If the points A(1, ‒2), B(2, 3), C(‒3, 2) and D(‒ 4, ‒ 3) are the vertices of parallelogram ABCD, then taking AB as the base, find the height of the parallelogram. CBSE 2013
Observe the graph given below and state whether ΔABC is scalene, isosceles or equilateral. Justify your answer. Also, find the area of ΔABC.
To raise social awareness about hazards of smoking, a school decided to start “NO SMOKING” campaign.10 students are asked to prepare campaign banners in the shape of triangle (as shown in the figure).
(i) If cost of 1cm2 of banner is ₹ 2, then find the overall cost incurred on such campaign.
(ii) Which mathematical concept is used in this question?
(iii) Which value is depicted in this question?
In a sports day celebration, Pushpraj and Shani are standing at positions A and B whose coordinates are (2, ‒ 2) and (4, 8), respectively. The teacher asked Deepanshi to fix the country flag at the mid-point of the line joining points A and B.
(i) Find the coordinates of the mid-point.
(ii) Which mathematical concept is used to solve the question?
(iii) What type of value is depicted here?