Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Standards: G-GPE.B.4, G-GPE.B.5, G-GPE.B.6, G-GPE.B.7 · Level: Grade 10 Geometry
Question 1 Distance and Midpoint (2 points)
Segment RS has endpoints R(−6, 2) and S(3, −4). Find its length as an exact simplified radical (1 point) and its midpoint (1 point).
Question 2 Parallel, Perpendicular or Neither (2 points)
Line a passes through (0, 4) and (6, 0). Line b passes through (−2, −5) and (4, −1). Line c passes through (1, 1) and (3, 4). Classify each pair: a and b (1 point); a and c (1 point).
Question 3 Line Through a Point (2 points)
Write, in slope-intercept form, the equation of the line through (4, −1) that is perpendicular to y = 43x + 2.
Question 4 Splitting a Segment (2 points)
Find the point P on segment AB with A(−6, 3) and B(14, −7) so that AP : PB = 2 : 3.
Question 5 Area and Perimeter (3 points)
Find the area (1 point) and the perimeter as an exact expression (2 points).
Question 6 Is It Isosceles? (3 points)
Prove that triangle KLM is isosceles and name the vertex angle.
Question 7 Prove a Parallelogram (3 points)
Prove that E(−2, 1), F(3, 0), G(6, 4) and H(1, 5) are the vertices of a parallelogram by finding the midpoints of both diagonals.
Question 8 Fourth Vertex (3 points)
Three vertices of a parallelogram are P(0, 0), Q(7, 2) and R(9, 7), taken in order. Find the fourth vertex S, and the area of the parallelogram.
