Q19 of 157 Page 724

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

In an isosceles triangle any two sides are equal.


AB = √{(– 2 – 7)2 + (5 – 10)2}


= √{(– 9)2 + (– 5)2}


= √{81 + 25}


= √{106}


BC = √{(– 4 – 5)2 + (3 – (– 2))2}


= √{(– 9)2 + (5)2}


= √{81 + 25}


= √{106}


AB = BC


∴ It is an isosceles triangle.


More from this chapter

All 157 →
17

If the point (x, y) is equidistant from the points (a + b, b – a) and (a – b, a + b), prove that bx = ay.

 18

Using the distance formula, show that the given points are collinear:

(i) (1, – 1), (5, 2) and (9, 5)


(ii) (6, 9), (0, 1) and (– 6, – 7)


(iii) (– 1, – 1), (2, 3) and (8, 11)


(iv) (– 2, 5), (0, 1) and (2, – 3).

 20

Show that the points A(3, 0), B(6, 4) and C(– 1, 3) are the vertices of an isosceles right triangle.

 21

If A(5, 2), B(2, – 2) and C(– 2, t) are the vertices of a right triangle with ∠B = 90°, then find the value of t.