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If two vertices of an isosceles right triangle are A(–1, –7) and B(–7, –1), then find coordinates of third vertex of the triangle ABC [Given ∠C = 90°]

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Asked on December 20, 2019 by

Sophie Rajora

The coordinates of base BC of an isosceles triangles ABC are given by B(1,3) and C(−2,7). Which of the following points can be the possible coordinates of the vertex A ?

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ANSWER

Given that ABC is an isosceles triangle.

The two vertices are B (1,3) = (x₂,y₂) and C (-2,7) = (x₂,y₂)

We have to find the co-ordinates of the vertex A

Since the triangle is an isosceles triangle So,

AB = AC ............. (1)

And also vertex A lies on y-axis.

Let A be (0,y) = (x₁,y₁)

Equation (1) ⇒ AB = AC

√ [(x₂ - x₁)² + (y₂ - y₁)²] = √ [(x₂ - x₁)² + (y₂ - y₁)²]

(1 - 0)² + (3 - y)² = (- 2 - 0)² + (7 - y)²

1 + (3 - y)² = 2 + (7 - y)²

1 + 9 + y² - 6y = 2 + 49 + y² -14y

10 - 6y = 51 - 14y

14y - 6y = 51 - 10

9y = 41

y=

9

41

y = 4.6

So, co-ordinates of the vertex A are A (0,4.6)