Analytical Geometry: Distance, Midpoint and Gradient — Worksheet & Memo

∑ DANEMATHICS

FREE CAPS MATHS RESOURCES

Grade 10 · Analytical Geometry

Analytical Geometry: Distance, Midpoint and Gradient

WORKSHEET

Name:

Class:

Date:

Mark

/ 29

Answer all questions. Show all your working — marks are awarded for method as well as the final answer.

1
Distance between (1 ; 1) and (4 ; 5). (distance)
(2)
2
Distance between (−2 ; 1) and (1 ; 5). (distance)
(2)
3
Midpoint of (2 ; 4) and (6 ; 10). (midpoint)
(2)
4
Gradient of the line through (1 ; 2) and (5 ; 10). (gradient)
(2)
5
Are gradients 3 and 3 parallel or perpendicular? (parallel)
(1)
6
What gradient is perpendicular to gradient 2? (perpendicular)
(1)
7
What gradient is perpendicular to gradient −3/4? (perpendicular)
(1)
8
Are (0 ; 0), (2 ; 4), (3 ; 6) collinear? (collinear)
(3)
9
Midpoint of (1 ; 2) and (x ; 8) is (4 ; 5). Find x. (unknown)
(2)
10
Distance from (0 ; 0) to (x ; 12) is 13 (x > 0). Find x. (unknown)
(3)
11
P(−1 ; 1), Q(3 ; 3), R(5 ; 7) and S(1 ; 5) are the vertices of a quadrilateral. Prove that PQRS is a parallelogram.
(4)
12
A(0 ; 0), B(4 ; 2) and C(2 ; 6). Show that AB ⊥ BC.
(3)
13
The diagonals of quadrilateral KLMN are KM and LN. K(1 ; 1), L(6 ; 2), M(7 ; 6), N(2 ; 5). Show that the diagonals bisect each other.
(3)

TOTAL: 29 marks