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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

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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.

We have, following given points

Fig. 7.23.
A(-1, -1)
B(-1, 4)
C(5, 4)
And D (5, -1)
Therefore, co-ordinates of P are

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Co-ordinates of Q are

equals straight Q open parentheses fraction numerator negative 1 plus 5 over denominator 2 end fraction comma fraction numerator 9 plus 4 over denominator 2 end fraction close parentheses rightwards double arrow straight Q space left parenthesis 2 comma space 4 right parenthesis

Co-ordinates of R are

equals straight R open parentheses fraction numerator 5 plus 5 over denominator 2 end fraction comma fraction numerator negative 1 plus 4 over denominator 2 end fraction close parentheses rightwards double arrow straight R open parentheses 5 comma 3 over 2 close parentheses

And, co-ordinates of S are

equals straight S open parentheses fraction numerator negative 1 plus 5 over denominator 2 end fraction comma fraction numerator negative 1 minus 1 over denominator 2 end fraction close parentheses rightwards double arrow straight S space left parenthesis 2 comma space 1 right parenthesis

Now,

Wee see that
PR = QR = RS = SP
and PR ≠ QS
Therefore PQRS is a rhombus.

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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).

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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.

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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.

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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