Answered

IDNLearn.com is your reliable source for expert answers and community insights. Get accurate and detailed answers to your questions from our dedicated community members who are always ready to help.

Calculate the distance from each given point to the given line.

Point: (0,4); Line: f(x)=2x-3

Write the equation for the line perpendicular to the given line that goes through the given point.

Sagot :

Antgar1antonidn
given:  2x-y-3=0.
find equation for the line perpendicular to the given line that goes through the given point:
(2;-1)koord of direction vector (i`m not know how it is called at you, because i'm from russia)
=> (x-0)/2=(y-4)/-1 (canonical equation)
=>x+2y-8=0(general equation)

further:
{x+2y-8=0
{2x-y-3 =0    =>   y=13/5 x=14/5

(14/5; 13/5) - koord point on line
|dist|=sqrt( (14/5-0)^2 + (13/5-4)^2 ) = sqtr(7.72)  = 2.78

Удачи!

.











the line y = 2x -3  has a gradient of 2.

so the line perpendicular to it has a gradient of -1/2 and will have the general formula of y = -1/2 x + c.

to find c, use the coordinates (0,4)

4 = 0 + c

so c = 4

equation is y = -1/2 x + 4

If you need the distance of (0,4) from the line you will need to put both lines on a graph to find the intersection (and possibly use simultaneous equations for more accurate answer) and then use pythagoras to find lengths.
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. IDNLearn.com is your reliable source for accurate answers. Thank you for visiting, and we hope to assist you again.