Question

Given ABC with A(-4, 1), B(8,-1), and C(-2, 9), write the equation of the line containing midsegment XZ In standard form where x is the midpoint of AB and Z is the midpoint of BC.

Answer 1

First, we will need to find the coordinates of X and Z as follows:
(1) X is the midpoint of AB
Xx-coordinate = (-4+8) / 2 = 2
Xy-coordinate = (1+-1)/2 = 0
The coordinates of point X are (2,0)

(2) Z is the midpoint of BC
Zx-coordinate = (8+-2) / 2 = 3
Zy-coordinate = (-1+9) / 2 = 4
The coordinates of point Z are (3,4)

Now, we will get the equation of the line containing points X and Z.
General form of a linear line is:
y = mx + c where:
m is the slope of the line
c is the y-intercept of the line

(a) The slope:
Slope = (y2-y1) / (x2-x1)
Slope = (4-0) / (3-2) = 4

(b) Y-intercept:
I will use the point (2,0), substitute with it in the equation and get c as follows:
y = mx + c
0 = 4(2) + c
c = -8

Based on the above calculations, the equation of the line containing points X and Z is:
y = 4x - 8

Answer 2

X would be halfway between A and B, so X is (2,0), averaging the coordinates([-4+8]/2,[1-1]/2). Z would be (3,4) as an average of B and C. Thus, we have the segment with a run of 1 (3-2) and a rise of 4 (4-0) so it has a slope of 4/1=4. However, we'd need to find the Y intercept to get an equation. If our y-intercept is -8, Y=-8*4x would be the formula. 0=-8+4*2, 4=-8*4*3 to confirm.