The endpoint of ab are a(4,3) and b (1,1) what are the coordinates of a” after the image has been translated (x, y) (x-5, y-1) and rotates 180 degrees about the origin?

A'' = (1, -2)

Step-by-step explanation:

First we apply the translation:

(4-5, 3-1) = (-1, 2)

Next we apply the rotation.  The rule for a 180 degree rotation is that every point (x, y) is mapped to (-x, -y):

(-1, 2) → (1, -2)

1 and 2

step-by-step explanation:

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)