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

Example 1 :

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

(1)  =  (2)

2/(a + 2)  =  2

2  =  2(a + 2)

2  =  2a + 4

2a  =  2 - 4

a  =  -1

So, the missing coordinate is -1.

Example 2 :

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

(-3/4) ⋅ [(b + 2)/6]  =  -1

-3(b + 2)/24  =  -1

b + 2  =  8

b  =  8 - 2  =  6

So, the missing coordinate is 6.

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