Question

ABC is an isoceles triangle. If the co-ordinates of the base are B(1,3) and C(2,7) then co-ordinates of vertex A can be?

Answer 1

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 = 41/9
y = 4.6
So, co-ordinates of the vertex A are A (0,4.6)
This is the required answer.
Thanks.