Answer:
1) Supports Jessie's Claim
2) Does Not Support Jessi's Claim
3) Supports Jessie's Claim
4) Does Not Support Jessi's Claim
Step-by-step explanation:
The given transformations are;
1) Rotation of 180° around the origin
For a rotation of 180° around the origin, either clockwise or anti clockwise, for a given coordinate of the preimage (x, y), the coordinate of the image is (-x, -y)
Therefore, whereby the slope of the preimage, given two points (0, 0) and (2, 2), = (2 - 0)/(2 - 0) = 1
For the image with the points (0, 0) and (-2, -2), we have;
(-2 - 0)/(-2 - 0) = 1
Therefore, the slope of the preimage and the image are equal
Therefore, supports Jessie's Claim
2) For a reflection across the line y = 2, we have
We note that the line y = 2 is parallel to the x-axis
For a reflection across the x-axis, for a preimage (x, y), we have the coordinates of the image (x, -y)
However for the reflection across the line y = 2, we have;
For a preimage, (x, y), the coordinate of the image is (x, -y+4)
Given two points, of the preimage (0, 0) and (2, 2), we have the image given as (0, 4) and (2, -2 + 4) = (2, 2);
The slope of the preimage is (2 - 0)/(2 - 0) = 1
The slope of the image is (2 - 4)/(2 - 0) = -1
The slope of the line of the preimage and the image are different
Therefore, does Not Support Jessi's Claim
3) For a translation up 1.25 units, we note that the difference in the y and x values of the coordinates of the preimage and the image will be equal when finding the slope, and therefore, the slope of the figure of the preimage and the slope of the figure of the image will be equal
Therefore, supports Jessie's Claim
4) For a reflection across the x-axis, a point on the preimage, with coordinates (x, y) will form a point on the image with coordinates (x, - y)
For a preimage with points (0, 0) and (2, 2), we have the image as (0, 0) and (2, -2)
The slope of the preimage is (2 - 0)/(2 - 0) = 1
The slope of the image is (-2 - 0)/(2 - 0) = -1
The slope of the line of the preimage and the image are different
Therefore, does Not Support Jessi's Claim
which simplifies to 
