Analytical Geometry: All the Exam Question Types — Worksheet & Memo

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Grade 10 · Analytical Geometry

Analytical Geometry: All the Exam Question Types

MEMORANDUM

Name:

Class:

Date:

Mark

/ 20

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

1
Distance between (1, 1) and (4, 5). (distance)
(2)
9+16 = 25 = 5✓✓ (2)
2
Distance between (−2, 1) and (1, 5). (distance)
(2)
9+16 = 5✓✓ (2)
3
Midpoint of (2, 4) and (6, 10). (midpoint)
(2)
((2+6)/2,(4+10)/2) = (4, 7)✓✓ (2)
4
Gradient of the line through (1, 2) and (5, 10). (gradient)
(2)
(10−2)/(5−1) = 2✓✓ (2)
5
Are gradients 3 and 3 parallel or perpendicular? (parallel)
(2)
Equal → parallel✓✓ (2)
6
What gradient is perpendicular to gradient 2? (perpendicular)
(2)
−12 (negative reciprocal)✓✓ (2)
7
What gradient is perpendicular to gradient −34? (perpendicular)
(2)
4⁄3✓✓ (2)
8
Are (0, 0), (2, 4), (3, 6) collinear? (collinear)
(2)
Gradients 2 and 2 → Yes✓✓ (2)
9
Midpoint of (1, 2) and (x, 8) is (4, 5). Find x. (unknown)
(2)
(1+x)/2 = 4 → x = 7✓✓ (2)
10
Distance from (0, 0) to (x, 12) is 13 (x > 0). Find x. (unknown)
(2)
x² + 144 = 169 → x = 5✓✓ (2)

TOTAL: 20 marks