isocsoles triangle help thanks for the help its appreciated?

Question

how do these points form an isosceles triangle (1, -3) (3,2) (-2,4)

i mean how do they show the vertices of the triangle

Answer 1

Let A = (1, -3), B= (3,2), C = (-2,4). Now, compute the length of the segments AB, BC and AC.

AB = sqrt((1 - 3)^2 + (-3 -2)^2) = sqrt(4 + 25) = sqrt(29).

Similarly,
BC = sqrt(5^2 + (-2)^2) ) = sqrt(29) and
AC = sqrt(3^2 + (-7)^2)) = sqrt(58)

So, AB = BC. These points do form a triangle, because it's immediate that AB < AC + BC and BC < AC + AB and AB + BC = 2 sqrt(29) = sqrt(4 * 29) > sqrt(2 *29) = sqrt(58) = AC. So, each side is less than the sum of the other 2, which is a necessary condition for these segments to actually form a triangle. It's important to check this.

So, we actually have an isosceles triangle. Sides AB and BC have the same length.

Answer 2

A=(1,-3)
B=(3,2)
C=(-2,4)
length of AB=sqrt (1-3)^2+(-3-2)^2=sqrt(4+25)=sqrt29
length ofBC=sqrt(3+2)^2+(2-4)^2=sqrt(25+4)=sqrt29
so AB=BC

Answer 3

I think those are the coordinates of the vertices, you'll need graph paper for that.