Q6 of 20 Page 52

Let us prove that the three points A(3, 3), B(8, –2) and C(–2, –2) are the vertices of a right-angled isosceles triangle. Let us calculate the length of the hypotenuse of ΔABC.

Given A → (3, 3)


B → (8, -2)


C → (-2, -2)


are the vertices of a triangle.


We know that distance between two points (x1, y1) and (x2, y2) is given by .


Using the above distance formula,


AB





BC




= 10


CA





Now, (AB)2 + (CA)2


and (AB)2


We find that (AB)2 + (CA)2 = (BC)2 and AB = CA.


Hence proved that the three points A(3, 3), B(8, –2) and C(–2, –2) are the vertices of a right-angled isosceles triangle.


Length of hypotenuse BC = 10 units.


More from this chapter

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4

Let us show that the points (7, 9), (3, –7) and (–3, 3) are the vertices of a right angled triangle by calculation.

 5

Let us prove that in both of the following cases, the three points are the vertices of an isosceles triangle:

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


(ii) (–2, –2), (2, 2) and (4, –4)

 7

Let us show by calculation that the points (2, 1), (0, 0), (–1, 2) and (1, 3) are the angular points of a square.

 8

Let us calculate and see that for what value of y, the distance of the two points (2, y) and (10, –9) will be 10.