Question

Given triangle QRS with Q(3, 7), R(-4,5), and S(2,-5), write an equation of median RA.

Answer 1

8x +13y = 33

Explanation:

The median RA will be the line through point R and point A, which is the midpoint of QS.

A = (Q +P)/2

A = ((3, 7) +(2, -5))/2 = (3+2, 7-5)/2 = (2.5, 1)

The slope of line RA is given by the slope formula ...

m = (y2 -y1)/(x2 -x1) = (1 -5)/(2.5 -(-4)) = -4/6.5 = -8/13

The y-intercept of line RA is given by ...

b = y1 -m(x1)

b = 5 -(-8/13)(-4) = 5 -32/13 = 33/13

Then the slope-intercept equation of line RA is ...

y = -8/13x +33/13

The standard form equation can be written as ...

13y = -8x +33

8x +13y = 33 . . . . . standard form equation of median RA