We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.

+0

# Question 14

0
183
1

I’ve tried so hard on this, can anyone do it?

The points A (6,1) and B(-2,5) are on the line with equation y=-1/2x+4

M is the midpoint of AB

Find an equation of the line through M that is perpendicular to y=-1/2x+4

Mar 18, 2018

### 1+0 Answers

#1
+3

Hi, I can help you :)

The points A (6,1) and B(-2,5) are on the line with equation y=-1/2x+4

M is the midpoint of AB

Find an equation of the line through M that is perpendicular to y=-1/2x+4

the gradient of the line   y=-1/2x+4   is    $$-\frac{1}{2}$$

The gradient of the line that is perpendicular is the negative reciprocal which is    $$+\frac{2}{1}=2$$

So 2 will be the gradient of the new line.

The midpoint of AB is simply  the average of the xes and the average of the ys

$$midpoint=(\frac{6+-2}{2},\frac{1+5}{2})\\ midpoint=(\frac{4}{2},\frac{6}{2})\\ midpoint=(2,3)\\$$

So you want the equation of the line through (2,3) with a gradient of 2

there are lots of methods to do this.

Here is one, my start is a bit different from normal, I think it makes it easier because it is the same for many different questions. You just need 2 different ways to express the gradient to make it work.

\begin{align} gradient &=gradient\\ m&=\frac{y-y_1}{x-x_1}\\ 2&=\frac{y-3}{x-2}\\ 2(x-2)&=y-3\\ 2x-4&=y-3\\ 2x-1&=y\\ y&=2x-1 \end{align}

I hope all that helps :)

Mar 18, 2018