Question

Given

ΔABC with A(−4,−2), B(4,4), and C(18,−8), answer the question.
Write the equation of the line containing the median that passes through point C in slope-intercept form.

Answer 1

To find the equation of the line containing the median that passes through point C, we first need to find the midpoint of segment AB. The coordinates of A and B are given as (-4, -2) and (4, 4) respectively, so we can find the x-coordinate of the midpoint by averaging the x-coordinates of A and B, and the y-coordinate of the midpoint by averaging the y-coordinates of A and B.

The midpoint is:

((-4+4)/2, (-2+4)/2) = (0, 1)

To find the slope of the median we will use the point slope form, which is:

y - y1 = m(x - x1)

We know that point C is (18, -8), and the midpoint is (0, 1)

The slope (m) will be:

m = (y2 - y1) / (x2 - x1) = (-8 - 1) / (18 - 0) = -9/18

We can now use point slope form and substitute the point and the slope:

y - (-8) = (-9/18) (x - 18)

To convert it to slope-intercept form we will solve for y:

y = (-9/18)x + (8/9 + 18/9) = -1/2x + 2

The equation of the line containing the median that passes through point C in slope-intercept form is y = -1/2x + 2