Question

The vertex A(-4,2) is a vertex of the triangle ABC. The edge BC lies on the line y=3x-7, and the height from the vertex C to the edge AB lies on the line y=2x+8. What are the coordinates of B and C of the triangle ABC?

Answer 1

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

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

Step-by-step explanation:

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