The first coordinate of M is -1.
Step-by-step explanation:
Given :- coordinates of F = (-4,-2) = (x1,y1)
coordinates of G = (2,-2) = (x2,y2)
coordinates of P = (2,-8) = (x3,y3)
and distance between point M and P is half of the distance between FG
To find :- first coordinate of point M
solution :- let the coordinate of M be (x4,y4)
as we know that distance between of the opposite point of parallel line segments are equal
so, second coordinate of M = -8
now by distance formula
FG = √(x2-x1)² + (y2-y1²)
= √[2-(-4)]² + [-2-(-2)]²
= √(2+4)² + (2-2)²
= √(6)² + (0)²
=√36
F G = 6
so, distance between point M and P = 1/2 × F G
= 1/2 × 6
= 3units
again, by distance formula
MP = √(x3-x4)² + (y3-y4)²
3 = √(2-x4)² + [-8-(-8)]²
squaring on both side
(3)² = (√(2-x4)² + [-8-(-8)]²)²
9 = (2-x4)² + [-8-(-8)]²
9 = (2-x4)²+(0)²
9 = (2-x4)²
√9 = 2-x4
3 = 2-x4
x4 = 2-3
x4 = -1
hence the first coordinate of M is -1
