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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