Question

right triangle def has vertices at d(0, 0) and e(10, 0). which best describes possible locations of point f?
a. any point on the line y = 10 except where x = 0
b. any point between d and e except where y = 0
c. any point on x = 10 except where y = 0
d. any point on the line y = 0 except where x = 10

Explanation:

Step1: Recall triangle - vertex properties

A triangle is formed by three non - collinear points. Points D(0,0) and E(10,0) lie on the x - axis (y = 0).

Step2: Analyze the third - vertex condition

For points D, E, and F to form a triangle, point F cannot be on the line segment DE. The line segment DE lies on the line y = 0 from x = 0 to x = 10. So, point F can be any point on the line y = 0 except where x is between 0 and 10 (i.e., except where x is on the line segment DE). In other words, any point on the line y = 0 except where x is in the open interval (0,10). This is equivalent to saying any point on the line y = 0 except where x = 0, x = 10 and x values between 0 and 10.

Answer:

A. Any point on the line y = 10 except where x = 0