Question

Pentagon ABCDE and pentagon A'B'C'D'E' are shown on the coordinate plane below: Pentagon ABCDE and pentagon A prime B prime C prime D prime E prime on the coordinate plane with ordered pairs at A negative 5, negative 2, at B negative 7, negative 3, at C negative 6, negative 6, at D negative 3, negative 5, at E negative 3, negative 3, at A prime 3, 6, at B prime 5, 5, at C prime 4, 2, at D prime 1, 3, at E prime 1, 5 Which two transformations are applied to pentagon ABCDE to create A'B'C'D'E'? Translated according to the rule (x, y) →(x + 8, y + 2) and reflected across the y-axis Translated according to the rule (x, y) →(x + 2, y + 8) and reflected across the x-axis Translated according to the rule (x, y) →(x + 2, y + 8) and reflected across the y-axis Translated according to the rule (x, y) →(x + 8, y + 2) and reflected across the x-axis

Answer 1

Translated according to the rule (x, y) →(x + 7, y + 1) and reflected across the x-axis.

We are given Pentagon ABCDE.

with vertices as:

A (-4,-2) , at B(-6,-3) at C (-5,-6), at D (-2,-5) at E (-2,-3)

and the pentagon A'B'C'D'E' with vertices as:

A'(3,1) , B'(1,2) , C'(2,5) , D'(5,4) and E'(5,2).

Clearly we could observe that the image is formed by the translation and reflection of the pentagon ABCDE.

First the Pentagon is translated by the rule:

(x,y) → (x+7,y+1) so that the pentagon is shifted to the fourth coordinate and then it is reflected across the x-axis to get the transformed figure in the first coordinate plane as Pentagon A'B'C'D'E

Hence, the answer is:

Translated according to the rule (x, y) →(x + 7, y + 1) and reflected across the x-axis

Question

Pentagon ABCDE and pentagon A'B'C'D'E' are shown on the coordinate plane below: Pentagon ABCDE and pentagon A prime B prime C prime D prime E prime on the coordinate plane with ordered pairs at A negative 4, negative 2, at B negative 6, negative 3, at C negative 5, negative 6, at D negative 2, negative 5, at E negative 2, negative 3, at A prime 3, 1, at B prime 1, 2, at C prime 2, 5, at D prime 5, 4, at E prime 5, 2 Which two transformations are applied to pentagon ABCDE to create A'B'C'D'E'? Translated according to the rule (x, y) →(x + 7, y + 1) and reflected across the x-axis Translated according to the rule (x, y) →(x + 1, y + 7) and reflected across the x-axis Translated according to the rule (x, y) →(x + 7, y + 1) and reflected across the y-axis Translated according to the rule (x, y) →(x + 1, y + 7) and reflected across the y-axis

Answer 2

The correct answer is:

Translated according to the rule (x, y) →(x + 2, y + 8) and reflected across the y-axis

Step-by-step explanation:

A translation using the rule (x, y) →(x + 2, y + 8) adds 2 to the x-coordinate and 8 to the y-coordinate. This takes our points and maps them the following way:

A(-5, -2)→(-3, 6)

B(-7, -3)→(-5, 5)

C(-6, -6)→(-4, 2)

D(-3, -5)→(-1, 3)

E(-3, -3)→(-1, 5)

The difference between each of these points and the image points is that the x-coordinates are negated. To do this, we would reflect the points through the y-axis.