Question

Need help with this please.

Answer 1

Answer:

$y = -\frac{3}{2} x + 4$

Step-by-step explanation:

First, let us find the gradient of AB:

Gradient of AB = $\frac{-1-3}{-1-5}$

                         = $\frac{2}{3}$

We also need to know that The product of gradients which are perpendicular to each other is -1. Using this idea, we can find the gradient of the perpendicular bisector:

(Gradient of perpendicular bisector)( $\frac{2}{3}$ ) = -1

Gradient of perpendicular bisector = $-\frac{3}{2}$

Now, we need to know at which coordinates the perpendicular bisector intersects AB. A perpendicular bisector bisects a line to two equal parts. Hence the coordinates of the intersection point is the midpoint of AB. Thus,

Coordinates of intersection = ( $\frac{-1 + 5}{2}$, $\frac{-1 + 3}{2}$ )

                                              = ( 2, 1 )

Now, we can construct our equation. The equation of a line can be formed using the formula $(y - y_{1}) = m(x - x_{1})$ where $m$ is the gradient and the line passes through $(x_{1} , y_{1} )$. Hence by substituting the values, we get:

$(y - 1) = -\frac{3}{2} (x - 2)$

$y - 1 = -\frac{3}{2} x + 3$

$y = -\frac{3}{2} x + 4$<u />