Coordinate Geometry practice questions

Secondary 3 topics from the O-Level Mathematics 4052 syllabus. Every question below has a full worked solution.

When a student gets a question wrong in Math Amigo, it does not show the answer straight away. It reads the working, identifies the step that went wrong, and asks a question that points at the correction. The worked solution is there once a genuine attempt has been made.

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What this topic covers

Worked examples

Example 1

Find the length of the line segment joining A(2,2)A(2, 2) and B(−1,8)B(-1, 8), giving your answer correct to 2 decimal places.
Show the worked solution
  • $AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$
  • $= \sqrt{(-1 - 2)^2 + (8 - 2)^2}$
  • $= \sqrt{(-3)^2 + 6^2}$
  • $= \sqrt{9 + 36}$
  • $= \sqrt{45}$
  • $= 3\sqrt{5} = 6.71 \text{ units (2 d.p.)} \quad \scriptsize\textit{simplify surd}$

Answer: 6.716.71

Example 2

The gradient of the line through (−1, k)(-1,\ k) and (0, −4)(0,\ -4) is 11. Find kk.
Show the worked solution
  • Gradient formula: $m = \dfrac{y_2 - y_1}{x_2 - x_1}$
  • $1 = \dfrac{-4 - k}{0 - (-1)}$
  • $1 = \dfrac{-4 - k}{1}$
  • $1 = -4 - k \quad \scriptsize\textit{multiply both sides by 1}$
  • $k = -4 - 1$
  • $k = -5$

Answer: −5-5

Example 3

A line passes through the point (1, −3)(1,\, -3) and has the same gradient as the line y=2x−1y = 2x - 1. Find the yy-intercept of this line.
Show the worked solution
  • The gradient of $y = 2x - 1$ is $m = 2$.
  • Our line also has gradient $2$, so its equation is $y = 2x + c$.
  • Substitute the point $(1,\, -3)$:
  • $-3 = 2(1) + c$
  • $-3 = 2 + c$
  • $c = -3 - 2 = -5$
  • $\therefore$ the $y$-intercept is $-5$.

Answer: −5-5

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Which syllabus does this follow?

O-Level Mathematics (4052), for Singapore secondary students. Math Amigo covers Secondary 1 to 4, both O-Level Mathematics and Additional Mathematics.

Will it just show my child the answer?

No. On a wrong answer it looks at the working, points to the step that went wrong, and asks a question that helps the student find the correction. The full worked solution is available after a genuine attempt.

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