In the diagram $R$ is the point $\left( 0,-4 \right)$ and $P$ is a point on the $y$-axis. Th

Question

In the diagram $R$ is the point $\left( 0,-4 \right)$ and $P$ is a point on the $y$-axis. The line $PQ$ meets the horizontal line through $R$ at $Q$. State the equation of $QR$. Given that the equation of the line $PQ$ is $2y-5x-4=0$, find the coordinates of $P$ and $Q$. Given that the length of $PQ$ is $\sqrt{t}$, find the value of $t$. Find the area of triangle $PQR$. Hence, calculate the perpendicular distance from $R$ to $PQ$.

Accepted Answer

(i) $y = -4$ (ii) $P(0, 2)$, $Q\left(-\frac{12}{5}, -4\right)$ (iii) $t = 41.76$ (iv) $7.2$ units$^2$ (v) $2.23$ units

Coordinate Geometry with Line Intersections and Perpendicular Distance

Coordinate Geometry with Line Intersections and Perpendicular Distance

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