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?
In order to prove that FP¯¯¯¯¯¯¯¯ is a median of △DEF, we need to show that F is the midpoint of DE.
To find the midpoint of a line segment with endpoints (x1, y1) and (x2, y2), we use the midpoint formula:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
In this case, the endpoints of DE are D(−6,4) and E(7,6).
Using the midpoint formula, we find that the midpoint of DE is:
((−6 + 7)/2, (4 + 6)/2)
= (1/2, 10/2)
= (1/2, 5)
Therefore, F(3,−7) is not the midpoint of DE. Therefore, the information about the coordinates of P alone cannot prove that FP¯¯¯¯¯¯¯¯ is a median of △DEF.