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

Answer:

$10|y|$

Step-by-step 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:

$|\frac{A_x(B_y-C_y)+B_x(C_y-A_y)+C_x(A_y-B_y)}{2}|$

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

$|\frac{5(y-0)+x(0-0)+25(0-y)}{2}|$

$|\frac{5(y)+x(0)+25(-y)}{2}|$

$|\frac{5y+0-25y}{2}|$

$|\frac{-20y}{2}|$

$|-10y|$

$10|y|$

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