Question

toby is learning to code using a programming language. he wants the code to transform triangle j to triangle k in the coordinate grid below. he starts by writing the steps he wants the code to take. then he will try to translate the steps into the programming language. tobys steps: 1) reduce size by 50%. 2) flip over the y - axis. analyze tobys steps. then write to toby and explain - whether his steps will map triangle j onto triangle k. - how can he rewrite his steps using words like reflect, dilate, translate, or rotate? - whether triangles j and k are congruent, similar, or neither.

Explanation:

1. First, reducing size by 50% is a dilation with a scale - factor of 0.5. Flipping over the y - axis is a reflection across the y - axis. These steps will map triangle J onto triangle K as the combination of dilation and reflection can transform one shape to the other as shown in the coordinate plane.
2. The steps can be rewritten as: "Dilate triangle J by a scale factor of 0.5, then reflect the resulting triangle across the y - axis."
3. Triangles J and K are similar. Since dilation changes the size of a figure (while maintaining the shape), and reflection is a rigid transformation that preserves shape and size of the dilated figure in terms of angles and angle - side relationships, the two triangles have the same shape but different sizes. Similar figures have the same shape but not necessarily the same size.

Answer:

• His steps will map triangle J onto triangle K.
• Rewritten steps: Dilate triangle J by a scale factor of 0.5, then reflect the resulting triangle across the y - axis.
• Triangles J and K are similar.