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

Explanation:

Step1: Recall properties of transformations

Rigid - motions (isometric transformations) preserve slope. Rigid - motions include translations, rotations, and reflections.

Step2: Analyze rotation of 180° around the origin

A rotation of 180° around the origin is a rigid - motion. It preserves the shape and orientation of the line segment in a way that the slope remains the same. So it supports Jessie's claim.

Step3: Analyze reflection across the line y = 2

A reflection across the line y = 2 is a rigid - motion. It flips the figure over the line y = 2 but does not change the relative steepness of the line segment, so the slope is preserved. It supports Jessie's claim.

Step4: Analyze translation up 1.25 units

A translation is a rigid - motion. Translating a line segment up or down (or in any direction) does not change its slope. It supports Jessie's claim.

Step5: Analyze reflection across the x - axis

A reflection across the x - axis is a rigid - motion. It flips the figure over the x - axis. The slope of a line segment changes its sign when reflected across the x - axis. If the original slope is $\frac{3}{4}$, after reflection across the x - axis, the slope of the new line segment will be $-\frac{3}{4}$. So it does not support 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: Does Not Support Jessie's Claim