# HOW TO CHECK IF TWO SIDES ARE PARALLEL WITH THE COORDINATES OF TRIANGLE

How to Check if Two Sides are Parallel with the Coordinates of Triangle :

Here we are going to see how to check if two two sides are parallel in triangle with given coordinates of triangle.

## How to Check if Two Sides are Parallel with the Coordinates of Triangle - Examples

Question 12 :

The vertices of triangle ABC are A(1, 8), B(-2, 4), C(8, -5). If M and N are the midpoints of AB and AC respectively, find the slope of MN and hence verify that MN is parallel to BC.

Solution :

If two lines are parallel, then slopes will be equal. Here the line joining the points AB and CD are parallel.

So, slope of AB  =  slope of CD Midpoint of the side AB  =  M

Midpoint of the side AC  =  N

Midpoint  =  (x1 + x2)/2, (y1 + y2)/2

A(1, 8), B(-2, 4), C(8, -5)

 Midpoint of AB :  =  (1 - 2)/2, (8 + 4)/2  =  -1/2, 12/2  =  M (-1/2, 6) Midpoint of AC :  =  (1 + 8)/2, (8 - 5)/2  =  9/2, 3/2  =  N (9/2, 3/2)

Slope of MN :

m  =  (y2 - y1)/(x2 - x1)

M(-1/2, 6) B(9/2, 3/2)

y2 - y=  (3/2) - 6

=  -9/2

x2 - x1  =  (9/2) + (1/2)

=  5

m  =  (-9/2)/5

m  =  -9/10 ----(1)

Slope of BC :

m  =  (y2 - y1)/(x2 - x1)

B (-2, 4) C (8, -5)

m  =  (-5 - 4)/(8 + 2)

m  =  (-9/10) ----(2)

(1)  =  (2)

Hence the sides BC And MN are parallel. After having gone through the stuff given above, we hope that the students would have understood, how to check if two sides are parallel with the coordinates of triangle.

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