Question

If vertices of a triangle are A (5, 0), B (x, y) and C (25, 0), what is the area of the triangle?(1) |x| = y = 10(2) x = |y| = 10

Answer 1

`10|y|`

Explanation:

We have been given that the vertices of a triangle are A (5, 0), B (x, y) and C (25, 0). We are asked to find the area of the given triangle.

We will use area formula for triangle with vertices A, B and C as given below:

`|(A_x(B_y-C_y)+B_x(C_y-A_y)+C_x(A_y-B_y))/(2)|`

Upon substituting the given coordinates of points A, B and C in above formula, we will get:

`|(5(y-0)+x(0-0)+25(0-y))/(2)|`

`|(5(y)+x(0)+25(-y))/(2)|`

`|(5y+0-25y)/(2)|`

`|(-20y)/(2)|`

`|-10y|`

`10|y|`

Therefore, the area of the given triangle would be
`10|y|`.