Question

Write the equation of the given line in standard form y=ax+b:

The line containing the midpoints of the legs of a right triangle ABC where A (-5,5), B (1,1) and C (3,4) are the vertices.

Answer 1

Find the distance between the sets of points.
Use this to determine which sides are the legs.

A to B = sqrt(52) = 7.2111
A to C = sqrt(50) = 7.07106
B to C = sqrt(65)= 8.622577

B to C is hypotenuse

midpoint of A to B is (-2,3)
midpoint of A to C is (-1, 4.5)

The line we are solving for contains these midpoints, so we have to solve for the slope between them and use point-slope form to make the equation of the line.
slope = 3/2 (or 1.5)
y=m(x-x1)+y1

y=3/2(x- (-2)) +3

y=3/2x+6