Right triangle xyz, has vertex angles at the coordinates, x(0, 0), y(-3, 0) and z(-3, 4) . its image, triangle x'y'z' has vertex angles at the coordinates, x'(3, -5), y'(0, -5), and z'(0, -1). describe the horizontal and vertical translations that map triangle xyz onto its image, triangle x'y'z'.

Right 3 ; down 5.

Step-by-step explanation:

Given a right triangle XYZ has vertex angles at the coordinates X(0,0),Y (-3,0)and Z(-3,4)

The vertex angles at the coordinates X'(3,-5) ,Y'(0,-5) and Z'(0,-1) of the image triangle X'Y'Z' of given triangle XYZ.

X(0,0) change into X'(3,-5)

We can write

x'-x=3-0=3

x'=x+3

y'-y=-5-0=-5

y'=y-5

Similarly , in the same way  Y(-3,0) change into (0,-5) and Z(-3,4) change into Z'(0,-1).

Hence, the horizontal translation x'=x+3 .It means shift 3 unit on the right side of x axis.

Vertical translation y'=y-5.It means shift 5 unit downward on the negative y-axis.

Option D. Right 3; down 5 is correct option.

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.