The equation of the perpendicular bisector of the line segment
joining the points (1 , 2) and (7 , 4) is y = -3x + 15
Step-by-step explanation:
Let us revise some rules
- The product of the slopes of the perpendicular lines is -1, that means one of them is additive and multiplicative inverse to the other. If the slope of one is m, then the slope of the other is
- The midpoint of a segment whose endpoints are and is
- The slope of a line that passes through points and is
∵ A line passes through points (1 , 2) and (7 , 4)
∴ = 1 and = 7
∴ = 2 and = 4
∴ The slope of the line =
To find the slope of the perpendicular bisector of this line reciprocal
its slope and change its sign
∵ The reciprocal of is 3
∴ The slope of the perpendicular bisector = -3
Let us find the mid point of the line
∵ = 1 and = 7
∵ = 2 and = 4
∴ The midpoint = = (4 , 3)
∵ The form of the equation is y = mx + b, where m is the slope of
the line and b is the y-intercept
∵ m = -3
∴ The equation of the line is y = -3x + b
- To find b substitute x and y in the equation by the coordinates
of the midpoint
∵ The coordinates of the midpoint are x = 4 and y = 3
∴ 3 = -3(4) + b
∴ 3 = -12 + b
- Add 12 to both sides
∴ 15 = b
∴ the equation of the perpendicular bisector is y = -3x + 15
The equation of the perpendicular bisector of the line segment
joining the points (1 , 2) and (7 , 4) is y = -3x + 15
Learn more:
You can learn more about the perpendicular lines in brainly.com/question/2601054
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