Question

If point S is located at (0, 0), point T is located at (0, 6), point U is located at (12, 0), and point V is located at (0, 10), what are the coordinates of point W that makes △STU ~ △SVW?

A. (0,20)
B. (0,24)
C. (20.0)
D.(24,0)

Answer 1

To find point W for similar triangles △STU and △SVW, calculate the necessary length to maintain the proportional sides. The horizontal distance VW should be 20 units, therefore point W will be at (20, 0).

Step-by-step explanation:

The question asks to find the coordinates of point W that makes △STU similar to △SVW. Since △STU has vertices S(0, 0), T(0, 6), and U(12, 0), and △SVW has vertices S(0, 0), V(0, 10), we need to find W such that the ratios of the corresponding sides are equal. The ratio of the heights (ST to SV) is 6/10 or 3/5. Since TU is horizontal and 12 units in length, we seek a point W such that VW is also horizontal and has length that maintains the same ratio. To preserve the similarity, VW should be (12 * 5/3) units long, which is 20 units. Hence, W should be 20 units to the right of V, which remains aligned with S and T on the y-axis. Therefore, the coordinates of W are (20, 0), making the correct answer Option C.