Question

I have math HW and these are the questions i wasn't aware of how to answer... please help.

a)Prove that 4x-y-1=0 is parallel to y=4x-5

b)Show that the points A(3,1), B(5,2) and C(11,5) are collinear

c)Show that the lines y=2x-4 and x+2y-10=0 are perpendicular to one other.

d) Prove that triangle ABC is isoscles given A(3,1), B(-3,7) and C(-1,3)

Thank you!

Answer 1

a) change the first into the form y = mx + b

4x - y - 1 = 0
-y = -4x + 1
y = 4x - 1
the value of m is the same for both equations, so they are parallel

b) find the slope between 2 different line segments.
If the slope is the same, then they are collinear.

c) slope of first is 2
After changing the second to the form y = mx + b, the value of m should be -1/2 to be perpendicular.

d) find the length of the 3 sides using your distance formula
Two of the lines should be the same