Marco is writing a coordinate proof involving a right isosceles triangle. marco places his triangle on the coordinate plane such that the base of the triangle lies along the x-axis. what coordinates should he assign to this third vertex of the isosceles triangle? (2a, 2b) (a, b) (b, a) (b, b)

Option B (a,b)

If you look at the peak of the  isosceles Triangle the y-axis coordinate should be b, and for x it should be a, since it is halfway between the a-axis, so a is the x-axis coordinate

Isosceles Triangle:

An Isosceles Triangle has the property of having two equal sides that means if side AC = AB then measure of angle ABC = angle of ABC This also means that segment AC is congruent to segment AB

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4

probably .5

i can on others if necessary.