# HOW TO FIND A MISSING COORDINATE IN AN ORDERED PAIR USING SLOPE

How to Find a Missing Coordinate in an Ordered Pair Using Slope :

Here we are going to see some practice questions based on slope.

## How to Find a Missing Coordinate in an Ordered Pair Using Slope - Examples

Question 10 :

The line joining the points A(-2 , 3) and B(a , 5) is parallel to the line joining the points C(0 , 5) and D(-2 , 1). Find the value of a.

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

 Slope of AB :m  =  (y2 - y1)/(x2 - x1)A(-2 , 3) and B(a , 5)m  =  (5 - 3)/(a + 2)m  =  2/(a + 2) ---(1) Slope of CD :m  =  (y2 - y1)/(x2 - x1)C(0 , 5) and D(-2 , 1)m  =  (1 - 5)/(-2 - 0)m  =  -4/(-2) m  =  2  ---(2)

(1)  =  (2)

2/(a + 2)  =  2

2  =  2(a + 2)

2  =  2a + 4

2a  =  2 - 4

a  =  -1

Hence the missing coordinate is -1.

Question 11 :

The line joining the points A(0, 5) and B(4, 2) is perpendicular to the line joining the points C(-1, -2) and D(5, b). Find the value of b.

Solution :

If two lines are perpendicular, then the product of slopes will be equal to -1.

slope of AB  slope of CD  =  -1

 Slope of AB :m  =  (y2 - y1)/(x2 - x1)A(0, 5) and B(4, 2)m  =  (2 - 5)/(4 - 0)m  =  -3/4  ---(1) Slope of CD :m  =  (y2 - y1)/(x2 - x1)C(-1, -2) and D(5, b)m  =  (b + 2)/(5 + 1)m  =  (b + 2)/6  ---(2)

(-3/4)  [(b + 2)/6]  =  -1

-3(b + 2)/24  =  -1

b + 2  =  8

b  =  8 - 2  =  6

Hence the missing coordinate is 6.

After having gone through the stuff given above, we hope that the students would have understood, how to find a missing coordinate in an ordered pair using slope

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