Q8 of 169 Page 644

Using the distance formula, show that the points A(3, -2), B(5, 2) and C(8,8) are collinear.

Given: The 3 points are A(3, -2), B(5, 2) and C(8, 8).

= 2√5 units …..(1)

= 3√5 units …..(2)

= 5√5 units …..(3)

From equations 1, 2 and 3, we have

⇒ AC = AB + BC

This is possible only if the points are collinear.

Therefore, the points A, B and C are collinear.

Hence, proved.

A is a point on the x-axis with abscissa -8 and B is a point on the y-axis with ordinate 15. Find the distance AB.

Find a point on the y-axis which is equidistant from A(-4, 3) and B(5, 2).

Show that the points A(7, 10), B(-2, 5) and C(3, -4) are the vertices of an isosceles right-angled triangle.

Show that the points A(1, 1), B(-1, -1) and C(-√3, √3) are the vertices of an equilateral triangle each of whose sides is 22 units.