List the points of the triangle if it were dilated by 2 times it’s size

Answers:

P ' (14, 6)

Q ' (12, 12)

R ' (18, 10)

Explanation:

The point P(7,3) moves to P'(14, 6) after multiplying the x and y coordinates by 2.

7*2 = 14

3*2 = 6

Similarly, Q(6,6) moves to Q'(12,12) following that same rule. Lastly, the point R(9,5) moves to R'(18,10)

The points are twice as far away from the origin compared to their preimage counterparts. This in turn makes the side lengths of triangle P'Q'R' to be twice as long compared to the corresponding side lengths of triangle PQR. Both triangles are different sizes, but the same shape. That makes them similar triangles (but they aren't congruent).

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.