Respuesta :
The equation of perpendicular bisector of QR is:
[tex]y = -\frac{2}{3}x+\frac{22}{3}[/tex]
Step-by-step explanation:
Given points are:
[tex]Q(-2,0)\ and\ R(6,12)[/tex]
First of all, we have to find the slope of the given line
So,
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
Here
(x1,y1) = (-2,0)
(x2,y2) = (6,12)
Let m1 be the slope of QR:
Then
[tex]m_1 = \frac{12-0}{6+2}\\= \frac{12}{8}\\= \frac{3}{2}[/tex]
Let m2 be the slope of perpendicular bisector
We know that the product of slopes of two perpendicular lines is -1
[tex]m_1.m_2 = -1\\\frac{3}{2}.m_2 = -1\\m_2 = -1 * \frac{2}{3}\\m_2 = -\frac{2}{3}[/tex]
The bisector will pass through the mid-point of QR
[tex]M = (\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2})\\M = (\frac{-2+6}{2}, \frac{0+12}{2})\\M = (\frac{4}{2}, \frac{12}{2})\\M = (2,6)[/tex]
Slope-intercept form of equation is:
[tex]y = m_2x+b[/tex]
Putting the value of slope
[tex]y = -\frac{2}{3}x+b[/tex]
Putting (2,6) in the equation
[tex]6 = -\frac{2}{3}(2)+b\\6 = -\frac{4}{3}+b\\b = 6+\frac{4}{3}\\b = \frac{18+4}{3}\\b = \frac{22}{3}[/tex]
So,
[tex]y = -\frac{2}{3}x+\frac{22}{3}[/tex]
Hence,
The equation of perpendicular bisector of QR is:
[tex]y = -\frac{2}{3}x+\frac{22}{3}[/tex]
Keywords: Mid-point, equation of line
Learn more about equation of line at:
- brainly.com/question/774670
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The equation of the perpendicular bisector of the segment with endpoints Q(−2,0) and R(6,12) is; y = -²/₃x + ²²/₃
We are given the endpoints of the segment as;
Q(-2, 0) and R(6, 12)
Coordinates of the midpoint of the segment is;
((-2 + 6)/2), ((0 + 12)/2)
⇒ (2, 6)
Now, the formula for the slope of the segment QR is;
m' = (y₂ - y₁)/(x₂ - x₁)
m' = (12 - 0)/(6 - (-2))
m' = 3/2
Now, the slope of the perpendicular bisector will be;
m = -1/m'
m = -1/(3/2)
m = -2/3
Thus, using equation of line in slope intercept form gives;
y = mx + c
y = -²/₃x + c
Let us put (2,6) for x and y respectively;
6 = -²/₃(2) + c
6 = -⁴/₃ + c
c = 6 + ⁴/₃
c = ²²/₃
Thus, equation of the perpendicular bisector of the segment with endpoints Q(−2,0) and R(6,12) is; y = -²/₃x + ²²/₃
Read more at; https://brainly.com/question/14353299
