Question

Consider triangle ABC with vertices A(0,0), B (0,6), and C (4,0). The image of triangle ABC after a dilation has vertices A'(0,0), B' (0,21), and C' (14,0).

What is the scale factor of the dilation?
k = ?

Answer 1

k=0.3

Explanation:

Let's call the length of each of the other two sides x. Since the triangle is isosceles, it has two sides of equal length. Therefore, the perimeter of the triangle can be expressed as 6 + x + x Simplifying this equation, we get 2x + 6 We know that the perimeter is 22 cm so we can set up an equation and solve for x. 22 = 2x + 6 Subtracting 6 from both sides, we get 16 = 2x Dividing both sides by 2, we get x=8