How to find reflection of a point about a line

Asked by admin @ in Mathematics viewed by 339 People

The point is the reflection of the point (- 7, 5) in the line 5x - 3y = 18 . Find the coordinates of P.

Answered by admin @


Answer:

Hello,

Step-by-step explanation:

slope of the line:

5x-3y=18\\\\y=\dfrac{5x-18}{3} \\\\slope=\dfrac{5}{3} \\\\\\slope\ of\ the\ perpendicular\ line=-\dfrac{3}{5} \\\\\\Equation\ of\ the\ perpendicular\ passing\ through\ (-7,5):\\\\y-5=(x+7)*\dfrac{-3}{5} \ or\ 5y-25=-3x-21 \ or\ 3x+5y=4\\\\\\\\Finding\ intersection\ of the\ line\ and\ the \ perpendicular:\\\\\left \{ \begin{array}{ccc}3x+5y&=&4\\5x-3y&=&15\\\end{array}\right.\\\\\left \{ \begin{array}{ccc}y&=&-1\\x&=&3\\\end{array}\right.\\\\\\

P'=(-7,5)

A=(3,-1)

\overrightarrow{P'A}=(3-(-7),-1-5)=(10,-6)

P=(3,-1)+(10,-6)=(13,-7)


Similar Questions

Find the equation of the tangent line at the point

Asked by admin @ in Mathematics viewed by 293 persons

What is the equation of the tangent line passing through the point (0, 3) of the graph of the function f(x) = x2 − 2x + 3?

How to find equation of a line with two points

Asked by admin @ in Mathematics viewed by 300 persons

How is the two point formula used to find the equation of a line when 2 points are known? a. taking the change in y over the change in x …

How to find the point slope equation of a line

Asked by admin @ in Mathematics viewed by 290 persons

Find the point-slope equation for the line that passes through the points (5, 19) and (-5, -1). Use the first point in your equation. please help :/ y- [?]=[?](x-[?])

Using two points to find the equation of a line

Asked by admin @ in Mathematics viewed by 317 persons

Writing Linear Equations Instruction Active Writing an Equation Given Two Points on the Line Write the equation of the line that passes through the points (7,-4) and (-1,3), first in …

Finding the slope of a tangent line at a point

Asked by admin @ in Mathematics viewed by 281 persons

Find the slope of the tangent line to the exponential function at the point (0,1) y=e^x/3

Find equation of a line with 2 points

Asked by maham237 @ in Mathematics viewed by 382 persons

How is the two point formula used to find the equation of a line when 2 points are known? a. taking the change in y over the change in x …

Find the slope of the line through each pair points

Asked by admin @ in Mathematics viewed by 419 persons

Find the slope of the line through each pair (1,-19),(-2,-7)

How to find the balance point on a number line

Asked by admin @ in Mathematics viewed by 300 persons

The number line shows how Isa's bank balance decreased after writing several checks. Which balance is \$86$86dollar sign, 86 more than the balance of -\$47.90−$47.90minus, dollar sign, 47, point, 90?

Find the equation of a line given slope and point

Asked by admin @ in Mathematics viewed by 349 persons

Point Slope Formula POS Write the equation of a line given two points. (1.3) and (-3,-5) First, find the slope between the two lines and enter that answer below. Remember …

Find the equation of a line given point and slope

Asked by admin @ in Mathematics viewed by 354 persons

Point Slope Formula POS Write the equation of a line given two points. (1.3) and (-3,-5) First, find the slope between the two lines and enter that answer below. Remember …

Find equation of a line given slope and a point

Asked by admin @ in Mathematics viewed by 349 persons

Point Slope Formula POS Write the equation of a line given two points. (1.3) and (-3,-5) First, find the slope between the two lines and enter that answer below. Remember …

Find the slope of the line containing the given points

Asked by admin @ in Mathematics viewed by 357 persons

Find the slope of the line that contains the following pairs of points (2,4) (0,8)

Find the slope of a line passing through 2 points

Asked by admin @ in Mathematics viewed by 293 persons

Which is the slope of the line that passes through the points (−3,1) and (4,−2)? Slope = -3 Slope = 1/2 Slope = -3/7 Slope = -7/3

Find the slope of a line passing through two points

Asked by admin @ in Mathematics viewed by 356 persons

Find the slope of the line that passes through the points shown in the table. The slope of the line that passes through the points in the table is what?

Find the points of trisection of the line segment joining

Asked by admin @ in Math viewed by 314 persons

Find the coordinates of the points of trisection of the line segment joining (4 -1) and (-2 -3)

Most viewed questions in Mathematics

Unit 6 similar triangles homework 2 similar figures answer key

Asked by maham237 @ in Mathematics viewed by 18341 persons

All things algebra unit 7 polygons and quadrilaterals answer key

Asked by admin @ in Mathematics viewed by 8139 persons

Gina wilson all things algebra 2016 answer key unit 11

Asked by admin @ in Mathematics viewed by 5764 persons

Unit 1 geometry basics homework 4 angle addition postulate answers

Asked by maham237 @ in Mathematics viewed by 3929 persons

Unit 6 exponents and exponential functions homework 8 answer key

Asked by maham237 @ in Mathematics viewed by 3246 persons

The manager of a vacation resort believes that the ages

Asked by maham237 @ in Mathematics viewed by 2918 persons

What is 271 403 rounded to the nearest ten thousand

Asked by maham237 @ in Mathematics viewed by 2779 persons

Unit 1 geometry basics homework 3 angle relationships answer key

Asked by maham237 @ in Mathematics viewed by 2572 persons

Homework 2 parallelograms

Asked by maham237 @ in Mathematics viewed by 2491 persons

Why would a prism beat a sphere in a competition?

Asked by maham237 @ in Mathematics viewed by 2473 persons

John wants to send a letter to peter

Asked by maham237 @ in Mathematics viewed by 2457 persons

An artist sells a painting for 20.50 but uses 5.75

Asked by maham237 @ in Mathematics viewed by 2423 persons

Unit 4 congruent triangles homework 1 classifying triangles answer key

Asked by maham237 @ in Mathematics viewed by 2413 persons

Unit 4 congruent triangles homework 2 angles of triangles

Asked by maham237 @ in Mathematics viewed by 2068 persons

Compare the values of the 2s and 5s in 55220

Asked by maham237 @ in Mathematics viewed by 1788 persons