Question

Two vertices of an isosceles triangle ABC with AB = AC are B(0, 6) and C(0, –2). If the area

of triangle ABC is 20 cm2

, then find the coordinates of A.​

Answer 1

Question :- Two vertices of an isosceles triangle ABC with AB = AC are B(0, 6) and C(0, –2). If the area of triangle ABC is 20 cm², then find the coordinates of A.

Solution :-

Let us assume that, the coordinates of A are (x , y).

given that,

• AB = AC .

so,

→ (x - 0)² + (y - 6)² = (x - 0)² + (y + 2)² { using distance formula .}

→ x² + y² + 36 - 12y = x² + y² + 4 + 4y

→ 36 - 12y = 4 + 4y

→ 4y + 12y = 36 - 4

→ 16y = 32

→ y = 2.

also, given that,

• Area of ∆ABC = 20 cm².

then,

→ (1/2)[x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)] = 20

→ [x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)] = 40

→ [x(6 + 2) + 0(-2 - 2) + 0(2 - 6)] = 40

→ 8x = 40

→ x = 5.

Hence, the coordinates of A are (5, 2) .

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