Question

Does any one know how to find the distance between the point (2,3) and the line 4x + 3y = 10?

Answer 1

First, find the equation of the line perpendicular to the given line that passes thorugh (2, 3).
Once you have the equation of the perpendicular, solve a system of equations of the two equations to find where the lines intersect.
Then, find the distance between the point of intersection and point (2, 3).

Answer 2

Could x=2 @mathstudent55

Answer 3

could that work?

Answer 4

Ok this is a big pain to solve, but here it is.
First put the equation of the line into y = m*x+b format
y = (4/3)x + 3.333
The perpendicular line will have slope -3/4 and passes through (2,3) so it's equation will be y = (-3/4)x+4.5

The two lines intersect at (.56,4.08)
The triangle with tip (.56,4.08) and right point at (2,3) has base 1.44 and height of 1.08
\[\sqrt{1.44^{2}+1.08^{2}} = 1.8 \]

1.8 is the answer

Answer 5

when they intersect i get (-2,6)?

Answer 6

What did you get for the equation of the perpendicular?

Answer 7

i plugged in the one that you had calculated

Answer 8

@Matt.Mawson calculated it, but I think he made a mistake.

Answer 9

Let's start from the beginning.
The given line is:
4x + 3y = 10

Answer 10

Solve it for y to get the slope:
3y = -4x + 10
y = (-4/3)x + 10/3

Answer 11

He made a mistake right in the beginning when he subtracted the 4x from both sides. It should be -4x on the right side, but he wrote 4x.

Answer 12

Yes i get that for my equation as well. and for my perpendicular i calculated y=(3/4)x +1.5

Answer 13

Yes, I have both of those.

Answer 14

for my point of intercept i have .88, 2.16

Answer 15

Yes, I got the same x and y as you.

Answer 16

so how will i find the distance?

Answer 17

The final step is the distance between (0.88, 2.16) and (2,3)

Answer 18

For that distance I get 1.4

Answer 19

yes i have that too... Okay. Thank You!

Answer 20

wlcm