yolandacoles3066
19.02.2021 •
Mathematics
"write an equation of the perpendicular bisector or the segment with endpoints Q(-2,0) and R(6,12). what does y equal?
Solved
Show answers
More tips
- H Health and Medicine How to Tan in a Tanning Bed? Tips and Recommendations...
- W Work and Career What is the Most In-Demand Profession in the Modern World?...
- A Auto and Moto How Can Parking Sensors Help Drivers?...
- H Health and Medicine What is the Normal Blood Sugar Level in a Healthy Person?...
- F Food and Cooking Red Caviar: How to Choose the Best?...
- C Computers and Internet Clearing Cache: How to Speed Up Your Browser...
- S Style and Beauty How are artificial nails removed?...
- S Style and Beauty Secrets of Tying a Pareo: 5 Ways...
- F Food and Cooking Everything You Need to Know About Pasta...
Answers on questions: Mathematics
- H History Many african americans during world war l...
- B Biology Treat these hœs like a tire i keep a spare...
- M Mathematics The figure shows a transversal t which intersects the parallel lines pq and rs: write a paragraph to prove that the measure of angle 4 is equal to the measure of angle 8....
- M Mathematics Can someone help me with this...
- M Mathematics A quadratic function is represented by the graph. (graph below.) (do a-d.) (a) What is the equation of the axis of symmetry of the function? (b) What are the coordinates of the...
Ответ:
The equation of perpendicular bisector of QR is:
y = -\frac{2}{3}x+\frac{22}{3}y=−32x+322
Step-by-step explanation:
Given points are:
Q(-2,0)\ and\ R(6,12)Q(−2,0) and R(6,12)
First of all, we have to find the slope of the given line
So,
m = \frac{y_2-y_1}{x_2-x_1}m=x2−x1y2−y1
Here
(x1,y1) = (-2,0)
(x2,y2) = (6,12)
Let m1 be the slope of QR:
Then
\begin{gathered}m_1 = \frac{12-0}{6+2}\\= \frac{12}{8}\\= \frac{3}{2}\end{gathered}m1=6+212−0=812=23
Let m2 be the slope of perpendicular bisector
We know that the product of slopes of two perpendicular lines is -1
\begin{gathered}m_1.m_2 = -1\\\frac{3}{2}.m_2 = -1\\m_2 = -1 * \frac{2}{3}\\m_2 = -\frac{2}{3}\end{gathered}m1.m2=−123.m2=−1m2=−1∗32m2=−32
The bisector will pass through the mid-point of QR
\begin{gathered}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)\end{gathered}M=(2x1+x2,2y1+y2)M=(2−2+6,20+12)M=(24,212)M=(2,6)
Slope-intercept form of equation is:
y = m_2x+by=m2x+b
Putting the value of slope
y = -\frac{2}{3}x+by=−32x+b
Putting (2,6) in the equation
\begin{gathered}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}\end{gathered}6=−32(2)+b6=−34+bb=6+34b=318+4b=322
So,
y = -\frac{2}{3}x+\frac{22}{3}y=−32x+322
Hence,
The equation of perpendicular bisector of QR is:
y = -\frac{2}{3}x+\frac{22}{3}y=−32x+322
Ответ: