Gradient between two points :
The gradient of a line is the slope of the line.
If given two points (x1, y1) and (x2, y2), then
Find the gradient
of the line segment joining the following pairs of points:
Problem 1 :
(2, 1) and (5, 2)
Solution :
Let A(2, 1) and B(5, 2) be the two points.
If A is (x1, y1) and B is (x2, y2), then
Slope of AB = (y2 – y1)/(x2 – x1)
Here x1 = 2, x2 = 5, y1 = 1, y2 = 2
= (2 – 1)/(5 – 2)
= 1/3
Problem 2 :
(5, 3) and (2, 2)
Solution :
Let A(5, 3) and B(2, 2) be the two points.
If A is (x1, y1) and B is (x2, y2), then
Slope of AB = (y2 – y1)/(x2 – x1)
Here x1 = 5, x2 = 2, y1 = 3, y2 = 2
= (2 – 3)/(2 – 5)
= -1/-3
= 1/3
Problem 3 :
(2, -2) and (4, 1)
Solution :
Let A(2, -2) and B(4, 1) be the two points.
If A is (x1, y1) and B is (x2, y2), then
Slope of AB = (y2 – y1)/(x2 – x1)
let x1 = 2, x2 = 4, y1 = -2, y2 = 1
= (1 + 2)/(4 – 2)
= 3/2
Problem 4 :
(7, 2) and (-3, 2)
Solution :
Let A(7, 2) and B(-3, 2) be the two points.
Slope of AB = (y2 – y1)/(x2 – x1)
Here x1 = 7, x2 = -3, y1 = 2, y2 = 2
= (2 – 2)/(-3 – 7)
= 0/-10
= 0
Problem 5 :
(-6, -2) and (-6, -4)
Solution :
Let A(-6, -2) and B(-6, -4) be the two points.
Slope of AB = (y2 – y1)/(x2 – x1)
Here x1 = -6, x2 = -6, y1 = -2, y2 = -4
= (-4 + 2)/(-6 + 6)
= -2/0
= undefined
Problem 6 :
(5, -1) and (-3, -3)
Solution :
Let A(5, -1) and B(-3, -3) be the two points.
Slope of AB = (y2 – y1)/(x2 – x1)
Here x1 = 5, x2 = -3, y1 = -1, y2 = -3
= (-3 + 1)/(-3 - 5)
= -2/-8
= 1/4
Problem 7 :
(-5, 4) and (4, 0)
Solution :
Let A(-5, 4) and B(4, 0) be the two points.
Slope of AB = (y2 – y1)/(x2 – x1)
Here x1 = -5, x2 = 4, y1 = 4, y2 = 0
= (0 – 4)/(4 + 5)
= -4/9
Problem 8 :
(0, -5) and (-2, -3)
Solution :
Let A(0, -5) and B(-2, -3) be the two points.
Slope of AB = (y2 – y1)/(x2 – x1)
Here x1 = 0, x2 = -2, y1 = -5, y2 = -3
= (-3 + 5)/(-2 – 0)
= 2/-2
= -1
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