Q7 of 48 Page 99

Prove that the points (2, –2), (–2, 1) and (5, 2) are the vertices of a right angled triangle.

We have A → (2, –2)


B → (–2, 1)


C → (5, 2)



Using the distance formula,














We find that (AB)2 + (CA)2 = (BC)2, or simply (5, 5, √50) forms a pythagorean triplet and hence the points A, B and C form a right angled triangle.


More from this chapter

All 48 →
5

Draw a quadrilateral, if its vertices are as follows:

(i) (1, 1), (2, 4), (8, 4) and (10, 1)


(ii) (–2, –2), (–4, 2), (–6, –2) and (–4, –6).


In each case tell the type of the quadrilateral.

 6

Find the distance between the following points:

(i) (–6, 7) and (–1, –5)


(ii) (–1, –1) and (8, –2)


(iii) (at12, 2at1) and (at22, 2at2)

 8

Prove that the points (1, –2), (3, 0), (1, 2) and (–1, 0) are the vertices of a square.

 9

Prove that the points (a, a), (–a, –a) and are the vertices of an equilateral triangle.