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Coordinate Geometry

Short Answer Type

151.

Let A (4, 2), B(6, 5) and C(1, 4) be the vertices of Δ ABC
What do yo observe?

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152.
Let A (4, 2), B(6, 5) and C(1, 4) be the vertices of Δ ABC
If A(x1 , y1), B(x2 , y2) and C(x3, y3 ) are the vertices of Δ ABC, find the coordinates of the centroid of the triangle

We know that the centroid of a triangle divides each median of the triangle from the vertex in the ratio 2 : 1. Let D be the mid-point of BC. Then,

Co-ordinates of D is

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Let G(x, y) be the centroid of ∆ABC. Then, G will divide AB internally in the ratio 2 : 1.

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Hence, the co-ordinates of the centroid are given by

open parentheses fraction numerator straight x subscript 1 plus straight x subscript 2 plus straight x subscript 3 over denominator 3 end fraction comma fraction numerator straight y subscript 1 plus straight y subscript 2 plus straight y subscript 3 over denominator 3 end fraction close parentheses.

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Long Answer Type

153. 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.

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Short Answer Type

154.

Find the distance between the points A and B in the following :

(i) A(2, 3), B(4, 1) (ii) A (a, b), B(-a, -b) (iii) A(5, -8); B(-7, -3)

(iv) A(4, 10), B(7, -6) (v) A (a + b, a - b), B(a - b, -a - b).

541 Views

155. Find the co-ordinates of the point which divides the line segment joining (4, -1) and (-2, 4) internally in the ratio 3 : 5.

181 Views

156. Find the co-ordinates of the point, which divides the line segment joining (5, -3) and (2, 3) internally in the ratio 1 : 2.

201 Views

157. Find the co-ordinates of the point which divides the line segment joining (2, 3) and (3, 4) internally in the ratio 3 : 2.

173 Views

158. Find the co-ordinates of the point which divides the line segment joining (-1, 3) and (4, -7) internally in the ratio 3 : 4.

196 Views

159. Find the co-ordinates of the point which divides the join of (-1, 7) and (4, -3) in the ratio 2 : 3.

1124 Views

160. Find the co-ordinates of the mid-points of the line joining the points (-2, -4) and (-3, 2).

122 Views

Previous Year Papers

Test Series

Test Yourself

Short Answer Type

152. Let A (4, 2), B(6, 5) and C(1, 4) be the vertices of Δ ABCIf A(x1 , y1), B(x2 , y2) and C(x3, y3 ) are the vertices of Δ ABC, find the coordinates of the centroid of the triangle

Long Answer Type

Short Answer Type

152.
Let A (4, 2), B(6, 5) and C(1, 4) be the vertices of Δ ABC
If A(x1 , y1), B(x2 , y2) and C(x3, y3 ) are the vertices of Δ ABC, find the coordinates of the centroid of the triangle