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

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

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

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

So, the missing coordinate is 6.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.

©All rights reserved. onlinemath4all.com

Recent Articles

  1. Digital SAT Math Problems and Solutions (Part - 213)

    Jul 13, 25 09:51 AM

    digitalsatmath292.png
    Digital SAT Math Problems and Solutions (Part - 213)

    Read More

  2. Digital SAT Math Problems and Solutions (Part - 212)

    Jul 13, 25 09:32 AM

    digitalsatmath290.png
    Digital SAT Math Problems and Solutions (Part - 212)

    Read More

  3. Digital SAT Math Problems and Solutions (Part - 211)

    Jul 11, 25 08:34 AM

    digitalsatmath289.png
    Digital SAT Math Problems and Solutions (Part - 211)

    Read More