Analytical Geometry is one of 9 topics in the Grade 11 Technical Mathematics CAPS syllabus, covered across 3 lessons on Study Vault. Below are real practice questions from this topic with full worked answers.
Sample practice questions
Easy
1. What is the formula for the gradient of a line through (x1;y1) and (x2;y2)?
m = (y2-y1)/(x2-x1)
m = (x2-x1)/(y2-y1)
m = (y2+y1)/(x2+x1)
m = y2-x2
Answer: m = (y2-y1)/(x2-x1) — The gradient formula is m = (y2-y1)/(x2-x1), the change in y divided by the change in x.
Easy
2. Find the gradient of the line through (1;3) and (4;9).
Answer: 2 — m = (9-3)/(4-1) = 6/3 = 2.
Medium
3. Find the equation of the line through (1;3) and (4;9), giving your answer in the form y = mx + c.
Answer: y = 2x + 1 — m = (9-3)/(4-1) = 2. Using (1;3): y-3=2(x-1), y=2x-2+3=2x+1.
