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Line L1 passes through the points A (1,2) and B (3, -4). Find the equation of L2 passing through the mid-point of AB and perpendicular to L1, leaving your answer in the form ax+by+c=0

Line L1 passes through the points A (1,2) and B (3, -4). Find the equation of L2 passing through the mid-point of AB and perpendicular to L1, leaving your answer in the form ax+by+c=0

Answers

Anthony
L1 passes through points A(1,2) and B(3,-4)

STEP 1

Find the gradient of L1

Gradient=dy/dx;
(-4-2)/(3-1)=-2
Gradient of L1 us -2

STEP 2

L2 is passing through the midpoint of AB;
Find the magnitude of AB by adding the contents of y in both points and contents of x in both points,then divide by 2 to get the midpoint

A+B=(1)+(3)
2 -4
A+B=(4)
-2
The midpoint =(4,-2)

STEP 3

Find the gradient of L2 perpendicular to L1

Gradient1xGradient2=-1(known)

Gradient1=-2
Gradient2=m;

-2m=-1
Divide by 2
m=1/2

STEP 4

Find the equation of L2 using the midpoint (2,-1) and gradient 1/2

{y-(-1)}/(x-2)=1/2

y+1/x-2=1/2

Cross multiply;

2y+2=x-2

Leaving your answer in form of ax+by+c=0;

x-2y=0...ans
muchira101 answered the question on February 14, 2019 at 11:01

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