Find the midpoint of the line segment with endpoints ( -1, 1 ) and ( 5, -5 )
1 answer:
Answer:
The answer is
<h2>( 2 , - 2)</h2>Step-by-step explanation:
The midpoint M of two endpoints of a line segment can be found by using the formula
where
(x1 , y1) and (x2 , y2) are the points
From the question the points are
( -1, 1 ) and ( 5, -5 )
The midpoint is
We have the final answer as
<h3>( 2 , - 2)</h3>Hope this helps you
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Answer:
y= -2x -8
Step-by-step explanation:
I will be writing the equation of the perpendicular bisector in the slope-intercept form which is y=mx +c, where m is the gradient and c is the y-intercept.
A perpendicular bisector is a line that cuts through the other line perpendicularly (at 90°) and into 2 equal parts (and thus passes through the midpoint of the line).
Let's find the gradient of the given line.
Gradient of given line
The product of the gradients of 2 perpendicular lines is -1.
(½)(gradient of perpendicular bisector)= -1
Gradient of perpendicular bisector
= -1 ÷(½)
= -1(2)
= -2
Substitute m= -2 into the equation:
y= -2x +c
To find the value of c, we need to substitute a pair of coordinates that the line passes through into the equation. Since the perpendicular bisector passes through the midpoint of the given line, let's find the coordinates of the midpoint.
Midpoint of given line
Substituting (-3, -2) into the equation:
-2= -2(-3) +c
-2= 6 +c
c= -2 -6 <em>(</em><em>-</em><em>6</em><em> </em><em>on both</em><em> </em><em>sides</em><em>)</em>
c= -8
Thus, the equation of the perpendicular bisector is y= -2x -8.