If square lmno is dilated by a scale factor of two about the center of the square to create square l'm'n'o', dilated line p'q' will (5 points) question 6 options: 1) be parallel to line pq and pass through point n 2) contain the points p and q 3) be perpendicular to line pq and pass through point l 4) shift two units to the right

Solution:

As given Square L M NO is dilated by  a scale factor of two about the center of the square to create square L'M'N'O'.

Original line of Dilation = Along P Q

New Dilated line = P'Q'

As scale factor > 1

1. Image Size > Pre image size

2. The two images will be similar.

3. Length of Dilated Line P' Q' = 2 × Length of PQ

As you can see from the diagram drawn below, Dilated line P'Q'  will contain the point P and Q.

All four points P,Q,Q',P' are collinear , lie in the same line.

Option (2) dilated line P'Q' will contain the points P and Q is true.

Line PQ is vertical thru the middle of the original square. The new square is dilated with a scale factor of 2 at the center, so the dilated line P'Q' would also be vertical running through the middle, so it would contain the points P and Q.

The answer is 2) contain the points P and Q

< 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)

2y+y=5

add 2y and y