Coordinate Geometry

Practise Coordinate Geometry for FBISE Grade 9–10 Mathematics (Grade 9–10): 3 multiple-choice questions with instant checking and worked explanations. Free, no sign-up.

FBISE Grade 9–10MathematicsGrade 9–103 questions

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Question 1

If a circle has centre (-4, 5) and passes through (1, -2), what is its radius?
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Answer: A) $74$
The radius of a circle is the distance from its centre to any point on the circle. Using the distance formula between $(- 4, 5)$ and $(1, - 2)$ gives $(1 + 4)^{2} + (- 2 - 5)^{2} = 5^{2} + (- 7)^{2} = 74$ , so the correct answer is $74$ . The option 13 comes from an arithmetic error in the distance calculation. The option 74 omits the square‑root, giving the squared distance. The option $85$ results from using an incorrect coordinate in the formula.
Question 2

If the line through (2, -1) and (k, 3) has slope 2, what is k?
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Answer: A) 4
The slope of a line through two points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ is $m = \frac{y _{2} - y _{1}}{x _{2} - x _{1}}$ . Substituting the given points $(2, - 1)$ and $(k, 3)$ and the given slope $2$ leads to $\frac{3 - ( - 1 )}{k - 2} = 2$ . Solving this equation gives $k = 4$ , which matches the marked correct answer. The option "0": The student reversed the denominator, using $\frac{y _{2} - y _{1}}{x _{1} - x _{2}}$ , which yields $k = 0$ . The option "2": The student mistakenly thought $k$ must equal the x‑coordinate of the first point, ignoring the slope formula. The option "6": The student made an algebraic error when expanding $2 (k - 2)$ , eventually arriving at $k = 6$ .
Question 3

The midpoint of the segment joining A(2, -3) and B(x, 5) is (5, 1). What is x?
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Answer: C) 8
The midpoint of a segment with endpoints $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ is $(\frac{x _{1} + x _{2}}{2}, \frac{y _{1} + y _{2}}{2})$ . Setting this equal to $(5, 1)$ and using the known coordinates gives $\frac{2 + x}{2} = 5$ , so $x = 8$ . The other options arise from common algebraic slips.

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Coordinate Geometry

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