Question

move △abc so it is a translation of △abc right 6 units and up 5 units. what would the slopes of the line segments from a to a, from b to b, and from c to c be? enter each slope in order, separated by commas.

Explanation:

Step1: Recall the property of translation

Translation is a rigid transformation, which means it preserves the shape and size of the figure. In terms of slopes of line segments, translating a figure does not change the slope of its sides because the horizontal and vertical changes (rise and run) between two points remain the same after translation.

Step2: Determine the slopes

Since translation preserves the slope, the slope of \( AA' \), \( BB' \), and \( CC' \) will be equal to the slope of the translation vector. The translation is 6 units right (run = 6) and 5 units up (rise = 5). The slope \( m \) is calculated as \( m=\frac{\text{rise}}{\text{run}} \).

So, the slope for each of these segments is \( \frac{5}{6} \).

Answer:

\(\frac{5}{6},\frac{5}{6},\frac{5}{6}\)