The coordinates of the vertices of the triangle shown are p (2, 13), q (7, 1) and r (2, 1). what is the length of segment pq in units?

To find the length or distance of two coordinates, we use pythagoras theorem
l² = Δx² + Δy²

Because we want to know the length of PQ, we use coordinate P and coordinate Q
(xp, yp) = (2,13)
(xq, yq) = (7,1)

Input the coordinates
l² = Δx² + Δy²
l² = (xp - xq)² + (yp - yq)²
l² = (2-7)² + (13-1)²
l² = (-5)² + (12)²
l² = 25 + 144
l² = 169
l = √169
l = 13

The length is 13 unit length