Answer:
Step-by-step explanation:
New Note 2
Given coordinates:
B(1,2)
E(-5,3)
A(-6,3)
Part A, isosceles triangle
Need to find lengths of sides
BE^2 = ((-5-1)^2+(3-2)^2) = 36+1 = 37
BA^2 = ((-6-1)^2+(-3-2)^2) = 49+25 = 74
EA^2 = ((-6-(-5))^2+(-3-3)^2) = 1+ 36 = 37
Since BE^2 = EA^2, BE=EA, or triangle BEA is isosceles, with vertex at E.
Part B, find point R so that BEAR is a sqare
Need to show that the vertex angle, BEA is a right angle.
BA is diagonal and E is 90° if
BE^2 + EA^2 = BA^2
or
37+37 = 74
Hence angle BEA is right anglesd, and the two legs are eaual with length sqrt(37)
To find point R, we find the translation from point E to point B, i.e. from the vertex to end of one of the legs.
EB = B - E = (1-(-5))-(2-3) = <6,-1>
To find point R, apply this translation to the end of the other leg, i.e. point A,
R=A(-6,-3) + <6,-1>=R(0,-4)
Check:
RE (diagonal)^2 = ((0-(-5))^2+(-4-3)^2) = 25+49 = 74 checks
RB^2 = ((0-1))^2+(-4-2)^2) = 1+36 = 37 checks
RA^2 = ((0--(-6))^2+(-4-(-3))^2) = 36+1 = 37 checks
