## LucyLu15 Group Title Does any one know how to find the distance between the point (2,3) and the line 4x + 3y = 10? one year ago one year ago

1. mathstudent55 Group Title

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).

2. LucyLu15 Group Title

Could x=2 @mathstudent55

3. LucyLu15 Group Title

could that work?

4. Matt.Mawson Group Title

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

5. LucyLu15 Group Title

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

6. mathstudent55 Group Title

What did you get for the equation of the perpendicular?

7. LucyLu15 Group Title

i plugged in the one that you had calculated

8. mathstudent55 Group Title

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

9. mathstudent55 Group Title

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

10. mathstudent55 Group Title

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

11. mathstudent55 Group Title

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.

12. LucyLu15 Group Title

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

13. mathstudent55 Group Title

Yes, I have both of those.

14. LucyLu15 Group Title

for my point of intercept i have .88, 2.16

15. mathstudent55 Group Title

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

16. LucyLu15 Group Title

so how will i find the distance?

17. mathstudent55 Group Title

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

18. mathstudent55 Group Title

For that distance I get 1.4

19. LucyLu15 Group Title

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

20. mathstudent55 Group Title

wlcm