Triangle ABC was translated according to the rule (x, y) → (x + 1.5, y – 3.5) to create the image ΔA'B'C' shown on the coordinate plane. Which graph shows the pre-image, ΔABC? On a coordinate plane, a triangle has points A prime (negative 1, 2), B prime (1, negative 1), C prime (negative 5, negative 1). On a coordinate plane, a triangle has points A (0.5, negative 1.5), B (0.5, negative 4.5), C (negative 3.5, negative 4.5). On a coordinate plane, a triangle has points A (2.5, 0.5), B (2.5, 2.5), C (negative 1.5, negative 2.5). On a coordinate plane, a triangle has points A (negative 4.5, 3.5), B (negative 4.5, 0.5), C (negative 8.5, 0.5). On a coordinate plane, a triangle has points A (negative 2.5, 5.5), B (negative 2.5, 2.5), C (negative 6.5, 2.5).

Step-by-step explanation:

Given:

ΔA'B'C' image.

A (-1,2)

B (-1,-1)

C (-5,-10)

rule of translation(x,y) → (x + 1.5,y - 3.5)

This means that the given coordinates are the the sum of x and the difference of y.

A:

-1 = x + 1.5  →  -x = 1.5 + 1 → -x = 2.5 → -x/-1 = 2.5/-1 → x = -2.5

2 = y - 3.5 → -y = -3.5 - 2 → -y = -5.5 → -y/-1 = -5.5/-1 → y = 5.5

A (-2.5 , 5.5)

B:

-1 =  x + 1.5  →  -x = 1.5 + 1 → -x = 2.5 → -x/-1 = 2.5/-1 → x = -2.5

-1 = y - 3.5 → -y = -3.5 + 1 → -y = -2.5 → -y/-1 = -2.5/-1 → y = 2.5

B (-2.5,2.5)

C:  

-5 = x + 1.5 → -x = 1.5 + 5 → -x = 6.5 → -x/-1 = 6.5/-1 → x = -6.5

-10 = y - 3.5 → -y = -3.5 + 10 → -y = 6.5 → -y/-1 = 6.5/-1 → y = -6.5

C (-6.5, -6.5)

The pre image will have the following coordinates:

A (-2.5 , 5.5) ; B (-2.5,2.5) ; C (-6.5, -6.5)

the answer is; biodiversity resulting from few ancestors

adaptive radiation occurs when a population is subjected to a large natural environment with spatial ecological variations. the parts of the population in the different ecologies begin to adapt to their local environments. due to non-random mating across the large populations, this causes the different populations from the large population to speciate within their local environments. they, therefore, diverge to different species sharing a common ancestor.