Question

jessie draws triangle abc on a coordinate grid. the slope of line - segment ab is $\frac{3}{4}$. jessie then transforms triangle abc using a single transformation to create triangle abc. she claims the slope of ab will still be $\frac{3}{4}$. for each transformation described, indicate whether it supports or does not support jessies claim.
rotation of 180° around the origin
reflection across the line y = 2
translation up 1.25 units
reflection across the x - axis
supports jessies claim
does not support jessies claim

Explanation:

Step1: Recall transformation - slope properties

Rigid - motions (translations, rotations, and reflections) preserve the shape and size of a figure, and also preserve the slopes of lines.

Step2: Analyze each transformation

Translation up 1.25 units

A translation is a rigid - motion. It just moves the triangle up without changing its orientation or the slopes of its sides. So, the slope of A'B' will be the same as the slope of AB.

Reflection across the line y = 2

A reflection is a rigid - motion. It flips the triangle over the line y = 2 but does not change the lengths of the sides or the angles between them. So, the slope of A'B' will be the same as the slope of AB.

Rotation of 180° around the origin

A rotation is a rigid - motion. It turns the triangle around the origin but preserves the shape and size of the triangle, including the slopes of its sides. So, the slope of A'B' will be the same as the slope of AB.

Reflection across the x - axis

A reflection is a rigid - motion. It flips the triangle over the x - axis but does not change the lengths of the sides or the angles between them. So, the slope of A'B' will be the same as the slope of AB.

Since all of these single transformations are rigid - motions and rigid - motions preserve slopes, each transformation supports Jessie's claim.

Answer:

Rotation of 180° around the origin: Supports Jessie's Claim
Reflection across the line y = 2: Supports Jessie's Claim
Translation up 1.25 units: Supports Jessie's Claim
Reflection across the x - axis: Supports Jessie's Claim