Question

quadrilateral abcd has vertices at a(2,3), b(8,4), c(12,2), and d(6,2). find the coordinates of the mid - point of bd.
coordinates: b( )

Explanation:

Step1: Recall mid - point formula

The mid - point formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})$.

Step2: Identify points for mid - point of BD

For points $B(8,4)$ and $D(6,2)$, let $(x_1,y_1)=(8,4)$ and $(x_2,y_2)=(6,2)$.

Step3: Calculate x - coordinate of mid - point

$x=\frac{8 + 6}{2}=\frac{14}{2}=7$.

Step4: Calculate y - coordinate of mid - point

$y=\frac{4+2}{2}=\frac{6}{2}=3$.

Answer:

$(7,3)$