A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 4 years ago
Can someone explain in steps how to solve this?
Find the image of the point P(2,1) under a reflection in the line x+y=4.
anonymous
 4 years ago
Can someone explain in steps how to solve this? Find the image of the point P(2,1) under a reflection in the line x+y=4.

This Question is Closed

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1327602494338:dw

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0What do I do next? I mean how to find x and y?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0we know that dw:1327602954262:dw

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0lines are perpendicular so their multiple of slope is 1 first lines' slope is 1 so second one's slope must be 1 m=(yy1)/(xx1) m=1 y1=1 x1=2 then y=x+1

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yeas, the answer i think might be (3,2). Plug x=2 into x+y=4 t get y=2, and then plug y=1 into x+y = 4 to get x=3. Now you can show that the gradient of the line passing through (3,2) and (2,1) is perpendicular to the gradient of your starting line x+y=4 by noting that \[x+y=4 \Longrightarrow y=x+4\] so the gradient is 1. On the other hand, the gradient of the line passing through (3,2) and (2,1) is given by \[\frac{21}{32} = \frac{1}{1} = 1\] The products of the gradients is 1x(1) = 1

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0y=4x y=x+1 so 4x=x+1 => x=3/2 =>y=5/2 (3/2,5/2) is coordinate of intersection so x changes 2 to 1,5 then it will decrease 1,5 to 1 y changes 1to 2,5 then it will increase 2,5 to 4 so P(1,4)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0sorry I made a mistake

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I didn't get the last part. :O

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1327604089388:dw

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0y=4x y=x1 so => y=3/2 =>x=5/2 (5/2,3/2) is coordinate of intersection so x changes 2 to 2,5 then it will decrease 2,5 to 3 y changes 1to 1,5 then it will increase 1,5 to 2 so P(3,2)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1327604371124:dw

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0The coordinates of intersection are: (5/2,3/2) so the distance from (2,1) to the mid point is equal to the distance from (3,2) to the midpoint: \[\sqrt{(5/22)^2 + (3/21)^2} = \sqrt{1} = \sqrt{(35/2)^2 + (23/2)^2}\] So the respective distances are equal, and both points: (2,1) and (3,2) lie on the line perpendicular to the mirror line, therefore they must be reflections of each other.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.