Question

what is the distance between point R at (6,3) and y=2x-6 ???

show work please

Answer 1

the closest y=2x+6 comes to 6,3 is 5,4... But the function is not one point...

Answer 2

but i think the distance is \[\sqrt{2}\]

Answer 3

k to find the distance think of the line connecting (6,3) with the line y = 2x - 6. it will be perpendicular to that line, because "distance" means minimum distance.

Answer 4

the equation for that line will have slope \[-\frac{1}{2}\] because it is perpendicular. and it will contain the point (6,3)

Answer 5

so the equation will be
\[y-3=-\frac{1}{2}(x-6)\]
\[y-3=-\frac{1}{2}x + 3\]
\[y = -\frac{1}{2}x+6\]

Answer 6

now we can find the point of intersection by setting the two lines equal and solving for x:
\[2x-6=-\frac{1}{2}x+6\]
\[4x-12=-x+12\]
\[5x=24\]
\[x=\frac{24}{5}\]

Answer 7

if you are still there you should check my algebra because i often make mistakes.

Answer 8

k

Answer 9

of course we are still not done. we know x, now find y and you will have the point on the line closest to (6,3) then you have to use the distance formula

Answer 10

ok so lets give dat a shot

Answer 11

hold on a second there may be something wrongn with my algebra

Answer 12

easier if i write it on paper. the line was y = 2x - 6 and the point is (6,3 )yes?

Answer 13

no it is good. the numbers coordinates are (4.8,3.6)

Answer 14

now distance formula yes?

Answer 15

yeah im ready sorry for takin long to replie i couldnt figuer out how to get back 2 dis page

Answer 16

1.34164 if we are working with decimals

Answer 17

no decimals in this

Answer 18

ok then i guess we work with the fractions

Answer 19

\[\sqrt{(6-\frac{24}{5})^2+(3-\frac{18}{5})^2}\]

Answer 20

how about i scan the work sheet on here u ok with that ill show u da question

Answer 21

\[\sqrt{(\frac{6}{5})^2+(\frac{3}{5})^2}\]

Answer 22

\[\sqrt{\frac{45}{25}}\]

Answer 23

\[\frac{3\sqrt{5}}{5}\]

Answer 24

sure but i like my answer

Answer 25

cool but jus look it look close

Answer 26

great! the answer is there and it is D because
\[\frac{3\sqrt{5}}{5}=\frac{3}{\sqrt{5}}\]

Answer 27

thank u so much!!!!