+0  
 
-1
28
3
avatar+72 

What is the intersection point of the line y = 2x + 5 and the line perpendicular to it that passes through the point (5,5)?

 Jun 30, 2020
 #1
avatar
-1

Equation of line: y = 2x + 5

Equation of perpendicuar line: y - 5 = 1/2(x - 5)

Intersection point: (-5/3, 5/3)

 
 Jun 30, 2020
 #2
avatar+72 
-2

that is wrong

 
 Jun 30, 2020
 #3
avatar+408 
+2

The line perpendicular to y=2x+5 must have the slope -1/2. We then have that the perpendicular line's equation is y=-1/2x+b. We plug in the given point (5, 5) to solve for b.

 

y=-1/2x+b

5=-1/2(5)+b

5=-5/2+b

b=15/2

 

So the equation of this line is y=-1/2x+15/2. To find the intersection point of it and y=2x+5, we set -1/2x+15/2 and 2x+5 to be equal to each other.

 

-1/2x+15/2=2x+5

5/2x=5/2

x=1

 

Plug this value into either of the equations for the lines we have. y=2x+5 will be easier to work with.

 

y=2x+5

y=2(1)+5

y=7

 

Therefore the intersection point is (1, 7).

 
 Jun 30, 2020

30 Online Users

avatar
avatar
avatar
avatar