Mathematics 4024 · O Level · Perpendicular lines

Perpendicular lines — practice question

(a)[2]

The triangle $PQR$ is isosceles, with $PR = QR$. $P$ is $(1,5)$ and $Q$ is $(5,1)$. $ ngle PRQ$ is not a right angle. Determine the coordinates of one possible location for $R$.

(b)[3]

Five curves are given by $y = 2 - x^2$, $y = x^3 - 2$, $y = x^2 + 2x - 8$, $y = x^3 - 3x$, and $y = x^2 - 3x$. Three of these graphs have been sketched. Put the right equation beneath each sketch.

(c)[5]

The coordinates of $A$ are $(-1,-5)$ and those of $B$ are $(3,3)$. Find the equation of the line that is perpendicular to $AB$ and passes through the midpoint of $AB$.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Any point in the form $(a,a)$, provided $a \ne 1,3,5$

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