SOLUTION: Indicate the equation of the given line in standard form. The line containing the altitude to the hypotenuse of a right triangle whose vertices are P(-1, 1), Q(3, 5), and R(5, -5)

Algebra ->  Parallelograms -> SOLUTION: Indicate the equation of the given line in standard form. The line containing the altitude to the hypotenuse of a right triangle whose vertices are P(-1, 1), Q(3, 5), and R(5, -5)      Log On


   

Question 468327: Indicate the equation of the given line in standard form.
The line containing the altitude to the hypotenuse of a right triangle whose vertices are P(-1, 1), Q(3, 5), and R(5, -5).
Place the symbols on the grid to complete the equation.
Answer by ccs2011(207) About Me  (Show Source):
You can put this solution on YOUR website!
First find which line segment refers to the hypotenuse:
Compute the following distances, PQ,PR,QR using the distance formula
d+=+sqrt%28%28x2-x1%29%5E2+%2B+%28y2-y1%29%5E2%29
You should find the following:
PQ = 5.65
PR = 8.48
QR = 10.19
Verify it is a right triangle by showing:
5.65%5E2+%2B+8.48%5E2+=+10.19%5E2
Therefore QR is the hypotenuse of this right triangle.
The altitude or height of this triangle is represented by PQ.
We need to determine the equation of the line passing through points P and Q.
Determine slope of the line by using slope formula:
m+=+%28y2-y1%29%2F%28x2-x1%29
P (-1,1) Q(3,5)
m+=+%285-1%29%2F%283-%28-1%29%29+=+4%2F4+=+1
slope of the line equals 1
Point-slope form:
(y -y1) = m(x - x1)
y+-+1+=+1%28x+-%28-1%29%29
y+-+1+=+x+%2B+1
y+=+x+%2B+2
Now it is in slope-intercept form
They want it in standard form: Ax + By = C
Just move the x to other side
Subtract x on both sides
-x+%2B+y+=+2