Q37 of 149 Page 14

Two opposite vertices of a square are (-1, 2) and (3, 2). Find the coordinates of other two vertices.

The coordinates are A(-1, 2) and C(3, 2).

Let the coordinates of the vertex B are (x, y)

AB = BC

Using distance formula =

On squaring both sides, we get

In ΔABC

AB² + BC² = AC² [Using Pythagoras theorem]

2AB² = AC² [Since AB = BC]

= 16

= 8

= 3

On substituting x = 1

= 3

= 0

= 0, 4

Other coordinates are (1, 0) and (1, 4)

Find the values of y for which the distance between the points P (2, -3) and Q (10, y) is 10 units.

Find the centre of the circle passing through (6, -6), (3, -7) and (3, 3).

Name the quadrilateral formed, if any, by the following points, and give reasons for your answers:

(i) A (-1, - 2), B (1, 0), C (-1, 2), D (-3, 0)

(ii) A (-3, 5), B (3, 1), C (0, 3), D (-1, - 4)

(iii) A (4, 5), B (7, 6), C (4, 3), D (1, 2)

Find the equation of the perpendicular bisector of the line segment joining points (7, 1) and (3, 5).