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ESAT Maths 1 Coordinate geometry questions

1 original ESAT Maths 1 coordinate geometry questions in the real exam style, each with a step-by-step worked solution and an explanation of why the tempting wrong answers are wrong. Try each one before opening the solution.

Methods on this page: Perpendicular bisector: equidistant from both points

Question 1ESAT Maths 1Standard

The perpendicular bisector of the line segment joining

A(4, 4)

and

B(-4, 1)

crosses the

y

-axis at

(0, k)

. What is

k

A $-\dfrac{5}{2}$
B $\dfrac{1}{2}$
C $\dfrac{3}{2}$
D $\dfrac{5}{2}$
E $\dfrac{7}{2}$
F $\dfrac{9}{2}$
G $\dfrac{11}{2}$

Show the answer and worked solution

Answer: D · Method: Perpendicular bisector: equidistant from both points

The midpoint of $AB$ is $(0, \dfrac{5}{2})$ and $AB$ has gradient $\dfrac{3}{8}$ , so the bisector has gradient $-\dfrac{8}{3}$ .
Alternatively: $(0, k)$ is the same distance from $A$ and $B$ .
$16 + (k - 4)^2 = 16 + (k - 1)^2$ gives $k = \dfrac{5}{2}$ .

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ESAT Maths 1 Coordinate geometry questions

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