The diagram shows an isosceles triangle $\Delta ABC$, where $AB = BC$ and the line segment

Question

The diagram shows an isosceles triangle $ABC$, where $AB = BC$ and the line segment $BC$ is parallel to the $y$-axis. Point $A$ lies on the $y$-axis and the equation of line $AC$ is $y = 2x + 3$.

Point $B$ is $(4, h)$, where $h$ is a positive constant.

Find the coordinates of $A$, $B$ and $C$.[4]
Given that the point $D$ is such that $ABCD$ is a kite, and the line segment $CD$ is parallel to the $x$-axis. Find the coordinates of $D$.[4]
Find the area of the kite $ABCD$.[2]

Accepted Answer

(a) $A=(0,3),\ B=(4,6),\ C=(4,11)$ (b) $D=(-6,11)$ (c) $50\text{ units}^2$

2025 AHS PRELIMS P2 Q3

2025 AHS PRELIMS P2 Q3

Solution:

Solution locked