The diagram shows a quadrilateral $ABCD$ with vertices $A(1, 5)$, $C(3, 1)$, and point $B$ l

Question

The diagram shows a quadrilateral $ABCD$ with vertices $A(1, 5)$, $C(3, 1)$, and point $B$ lies on the $x$-axis. $BD$ intersects $AC$ at $M$. It is given that $BD$ is the perpendicular bisector of $AC$ and $CD$ is parallel to the $y$-axis. Find the equation of $BD$,[3] the coordinates of $B$ and of $D$,[3] the area of $ABCD$.[2]

Accepted Answer

(a) $y = \frac{1}{2}x + 2$; (b) $B(-4, 0)$, $D\left(3, \frac{7}{2}\right)$; (c) $17\frac{1}{2}$ units$^2$

2023 ACSBR AM S3 EOY Q10

2023 ACSBR AM S3 EOY Q10

Video Solution:

Solution:

Handwritten & Typed Solutions