The vertices of ΔPQR are P(2, 1), Q(–2, 3) and R(4, 5), then equation of median through vertex R is:-

The median of a triangle is a line segment joining a vertex to the midpoint of the opposite side.

Step 1: Find the midpoint of PQ The midpoint formula is ((x1+x2)/2, (y1+y2)/2).

So, the midpoint of PQ, let's call it M, is ((2-2)/2, (1+3)/2) = (0, 2).

Step 2: Find the equation of the line RM The slope formula is (y2-y1)/(x2-x1).

So, the slope of RM, let's call it m, is (2-5)/(0-4) = -3/4.

Step 3: Use the point-slope form of a line equation The point-slope form is y - y1 = m(x - x1).

Substituting the point R(4,5) and the slope m=-3/4 into the equation, we get:

y - 5 = -3/4 * (x - 4)

Step 4: Simplify the equation Multiply through by 4 to get rid of the fraction:

4y - 20 = -3x + 12

Rearrange to get the equation in standard form:

3x + 4y = 32

So, the equation of the median through vertex R is 3x + 4y = 32.