Triangle DEF has vertices D(−6,4), E(7,6), and F(3,−7). Which information about the coordinates of P will prove that FP¯¯¯¯¯¯¯¯ is a median of △DEF?
A. P(1,5)
B. P(0,3)
C. P(0.5,5)
D. P(1,1)
To prove that FP¯¯¯¯¯¯¯¯ is a median of △DEF, we need to show that it passes through the midpoint of the side DE.
The midpoint of the side DE can be found by taking the average of the x-coordinates and the average of the y-coordinates of D and E.
Midpoint of DE = [(x-coordinate of D + x-coordinate of E)/2, (y-coordinate of D + y-coordinate of E)/2]
= [(-6 + 7)/2, (4 + 6)/2]
= [1/2, 10/2]
= [1/2, 5]
Therefore, the coordinates of the midpoint of DE is P(1/2, 5).
The only answer choice that matches the coordinates of the midpoint of DE is C. P(0.5,5).
Therefore, the answer is C. P(0.5,5).