Answer:
a. [tex]M(x,y) = (-1,-1)[/tex]
b. [tex]D(-4,-9)[/tex]
Step-by-step explanation:
Given
A(-8,7) and B(6,-9).
Solving (a):
Determine the Midpoint M;
This is calculated as follows;
[tex]M(x,y) = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
Where
[tex](x_1,y_1) = (-8,7)[/tex]
[tex](x_2,y_2) = (6,-9)[/tex]
Substitute these values in the formula
[tex]M(x,y) = (\frac{-8+6}{2},\frac{7-9}{2})[/tex]
[tex]M(x,y) = (\frac{-2}{2},\frac{-2}{2})[/tex]
[tex]M(x,y) = (-1,-1)[/tex]
Hence; the midpoint is (-1,-1)
Solving (a):
Here, we have
C = (2,7)
M; Midpoint = (-1,-1)
Required: Determine D
This is calculated as follows;
[tex]M(x,y) = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
Where
[tex](x_1,y_1) = (2,7)[/tex]
[tex](x,y) = (-1,-1)[/tex]
Substitute these values in the formula
[tex](-1,-1) = (\frac{2+x_2}{2},\frac{7+y_2}{2})[/tex]
Solving for x2
[tex]-1 = \frac{2 + x_2}{2}[/tex]
Multiply both sides by 2
[tex]-2 = 2 + x_2[/tex]
Subtract 2 from both sides
[tex]x_2 = -2 - 2[/tex]
[tex]x_2 = -4[/tex]
Solving for y2
[tex]-1 = \frac{7 + y_2}{2}[/tex]
Multiply both sides by 2
[tex]-2 = 7 + y_2[/tex]
Subtract 7 from both sides
[tex]y_2 = -2 - 7[/tex]
[tex]y_2 = -9[/tex]
Hence, the coordinates of D is
[tex]D(-4,-9)[/tex]
