Point M is located in the third quadrant.
The distance between point M and point P is half the distance between point F and
point G.
• Segment MP is parallel to segment FG.
What is the first coordinate of point M?
A. -10
B. -8
C. -2
D. -1

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

answer: 2530

hope this