Given ΔABC with A(–3, 4), B(5, 8), and C(2, –2), 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. (1 point)
To find the coordinates of X and Z, we need to find the midpoint of AB and BC.
The midpoint of AB can be found by taking the average of the x-coordinates and the average of the y-coordinates:
Midpoint(X) = ((-3 + 5)/2, (4 + 8)/2) = (1, 6)
The midpoint of BC can be found in the same way:
Midpoint(Z) = ((5 + 2)/2, (8 - 2)/2) = (7/2, 3)
Now we have the coordinates of X and Z, and we can find the equation of the line containing XZ.
First, let's find the slope of XZ. The slope formula is given by:
m = (y_2 - y_1)/(x_2 - x_1)
Using the coordinates of X(1, 6) and Z(7/2, 3), we have:
m = (3 - 6)/(7/2 - 1) = -3/(3/2) = -2
Now we can use the point-slope form of a linear equation, y - y_1 = m(x - x_1), using the point (1, 6):
y - 6 = -2(x - 1)
Simplifying, we get:
y - 6 = -2x + 2
Now, let's rewrite this equation in standard form, Ax + By = C:
2x + y = 8
So, the equation of the line containing midsegment XZ is 2x + y = 8. Answer: \boxed{2x + y = 8}.