SOLUTION: HI! I have a math homework on linear equations, and I am stuck at question number 2. Here goes the problem: Given the point A(2,7) and the line l1 with equation 3x – 4y – 8 =

Algebra ->  Linear-equations -> SOLUTION: HI! I have a math homework on linear equations, and I am stuck at question number 2. Here goes the problem: Given the point A(2,7) and the line l1 with equation 3x – 4y – 8 =       Log On


   

Question 1024690: HI!
I have a math homework on linear equations, and I am stuck at question number 2.
Here goes the problem:
Given the point A(2,7) and the line l1 with equation 3x – 4y – 8 = 0
1. Find equation of the line AQ, which is perpendicular to l1 and passing through A.
2. Find the coordinates of point Q, which is the point of intersection between the line AQ and the line l1.
3. Calculate the length of [AQ].
4. On graph paper, plot the point A(2,7) and the line l1 with equation 3x – 4y – 8 = 0.
From point A, draw a perpendicular to the line l1. Let Q be the point of intersection between the perpendicular and the line l1. From your graph, measure the length [AQ] and compare it with the distance you previously calculated.
I have solved the first one and my answer is y= -4/3X + 25/3
As for questions number 4, I would appreciate it if you gave me some tips on how to draw the graph
Thanks in advance!!
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Your answer to number 1 is sort of on the right track but your value for the constant term in the equation is off.

Your calculation of the slope of the perpendicular is correct, so I won't repeat that. Knowing a point on a line and the slope, use the point-slope form:











2. If point is on both lines, then since



and



then



I'll let you convince yourself that and then

3. Use the distance formula



4.



John

My calculator said it, I believe it, that settles it