ACSEE (Form 6) Coordinate Geometry I — practice questions

Explore 3 free Coordinate Geometry I questions in ACSEE (Form 6) Advanced Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Coordinate Geometry I questions and exercises with answers

Showing questions 1–3 of 3.

The perpendicular distance from the point $(-2,-3)$ to the line $12x+16y+12=0$ is:Read the answer and worked solution →Complete the circle methodRead the answer and worked solution →Distance from a point to a lineRead the answer and worked solution →

Worked practice questions

The perpendicular distance from the point $(-2,-3)$ to the line $12x+16y+12=0$ is:

2 units
3 units
5 units
6 units

Show answer and solution

Correct answer: B. 3 units

1. Use $d=\left|\dfrac{Ah+Bk+C}{\sqrt{A^2+B^2}}\right|$ with $A=12$, $B=16$, $C=12$. 2. Numerator: $12(-2)+16(-3)+12=-24-48+12=-60$. 3. Denominator: $\sqrt{12^2+16^2}=\sqrt{144+256}=\sqrt{400}=20$. 4. $d=\left|\dfrac{-60}{20}\right|=3$ units. 5. Forgetting the modulus or dropping the constant term $12$ produces the other values. _Source: NECTA ACSEE 2023 Advanced Mathematics 142/1, Question 8: Coordinate Geometry I_

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Complete the circle method

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Missing parts

Answer
one
Choices
1. one
2. two
3. zero
Answer
(−g, −f)
Choices
1. (−g, −f)
2. (g, f)
3. (2g, 2f)
Answer
√(g²+f²−c)
Choices
1. √(g²+f²−c)
2. g²+f²−c
3. √(g²+f²+c)

Complete the statement

Before reading off the centre, divide so the coefficients of x² and y² are {0}. The centre is then {1} and the radius is {2}.

Instructions

Tap the right word into each blank.

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Distance from a point to a line

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Questions

Hint
|Ah + Bk + C| ÷ √(A²+B²)
Unit
units
Answer
3
Question
Distance from (−2, −3) to 12x + 16y + 12 = 0
Hint
√(g² + f² − c)
Unit
units
Answer
9
Question
Radius of x² + y² + 4x + 6y − 68 = 0

Instructions

Work it out and key in the answer.

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