Exam (elaborations) mathematics

Grade 10 Analytical Geometry Test
Time: 60 minutes
Total Marks: 50



Question 1: Distance Between Two Points (5 marks)
Calculate the distance between the points A(2,−3)A(2, -3)A(2,−3) and B(6,5)B(6, 5)B(6,5).



Question 2: Midpoint of a Line Segment (5 marks)
Find the midpoint of the line segment joining the points C(−4,2)C(-4, 2)C(−4,2) and D(8,−6)D(8, -
6)D(8,−6).



Question 3: Gradient (Slope) of a Line (5 marks)
Determine the gradient of the line passing through the points E(1,7)E(1, 7)E(1,7) and F(4,−2)F(4, -
2)F(4,−2).



Question 4: Equation of a Line (10 marks)
Given the points G(2,3)G(2, 3)G(2,3) and H(6,7)H(6, 7)H(6,7):
a) Find the gradient of the line GH. (3)
b) Write the equation of the line GH in the form y=mx+cy = mx + cy=mx+c. (4)
c) Does the point P(10,11)P(10, 11)P(10,11) lie on the line? Show working. (3)



Question 5: Parallel and Perpendicular Lines (10 marks)
a) Find the gradient of the line with the equation y=2x−5y = 2x - 5y=2x−5. (2)
b) Determine the gradient of a line perpendicular to this one. (2)
c) Write the equation of a line that is parallel to the one in (a) and passes through the point
Q(1,4)Q(1, 4)Q(1,4). (3)
d) Write the equation of a line perpendicular to the one in (a) that passes through the point
R(2,1)R(2, 1)R(2,1). (3)



Question 6: Properties of Geometric Figures (15 marks)
The vertices of quadrilateral ABCDABCDABCD are:
A(1,2),B(5,6),C(9,2),D(5,−2)A(1, 2), B(5, 6), C(9, 2), D(5, -2)A(1,2),B(5,6),C(9,2),D(5,−2)
a) Show that AB∥CDAB \parallel CDAB∥CD by comparing gradients. (4)
b) Show that AD∥BCAD \parallel BCAD∥BC. (4)
c) Prove that ABCDABCDABCD is a parallelogram. (3)
d) Calculate the length of diagonal ACACAC. (4)