In an isosceles triangle, the perimeter is 8 more than 2 times on of the legs. If the perimeter is 28 in, find the length of the base.

Question

A. 16 in
B. 18 in
C. 10 in
D. 8 in

Given triangle ABC with A(-3, 2), B(-1, -4), and C(4, 1), write the equation for the line containing altitude line AR in standard form.

A. x - y = 1
B. x + y = -1
C. x + y = 1
D. x - y = -1

Given triangle ABC with A(-3, 4), B(5, 8), and C(2, -2), write the equation of the line containing midsegment line XZ in standard form, where X is the midpoint of line AB and Z is the midpoint of line BC.

A. 6x - 5y = -24
B. 2x + 5y = 32
C. 2x - 5y = -28
D. 6x + 5y = 36

What is the image of O(-2, -1) after two reflections, first across the line y = -5, then across the line x = 1?

A. (-2, -1)
B. (-1, -6)
C. (4, -9)
D. (1, -5)

These are the only questions that I need help on for this test! I can't seem to solve them, I really need help!!! Please help? Thanks!

Answer 1

In any isosceles triangle, the perimeter is the base plus 2 times one of the legs. Clearly the base here is 8.

No idea where R is.

X = (A+B)/2 = (1,6)
Z = (B+C)/2 = (7/2,3)
XZ in two-point form is
y-6 = (-6/5)(x-1)
Now just rearrange that into standard form.

across y = -5: (x,y)->(x,-10-y)
across x = 1: (x,y)->(2-x,y)
both: (x,y)->(2-x,-10-y)
So, (-2,-1)->(4,-9)

Answer 2

Thanks Steve!
(But I STILL need help figuring out the AR one... gonna repost that question)

Answer 3

the amount of people who have seen this but havent said dip ship