Now, to show that the line through (2, 3) and (7, -7) is perpendicular to the line through (3, 3) and (-2, 2), we have to find the slopes of both lines first, so

Slope of line 1 = m1 = (- 7 - 3)/(7 - 2) = - 10/5 = - 2

Slope of line 2 = m2 = (2 - 3)/(- 2 - 3) = - 1/(- 5) = 1/5

Now if the product of both slopes becomes - 1, then this means that they are perpendicular otherwise not. so

= m1 * m2

= - 2 * 1/5

= - 2/5

Hence the product is not equal to - 1, So the lines are not perpendicular to each other.