Question

1. select the correct transformation for each diagram.

translation
reflection
rotation
translation
reflection
rotation

1. given alp and alp answer the following questions:

a. describe the transformation from △alp→△alp using the coordinates(x,y)
a: ( , ) a: ( , )
l: ( , ) l: ( , )
p: ( , ) p: ( , )
b. write the rule for the transformation
(x, y)→( , )
c. perform the transformation to alp for the given rule (plot it)
(x, y)→(x - 4,y + 1).

Explanation:

Step1: Analyze first - diagram transformation

The first diagram shows a figure where each point of the red - colored polygon is moved to a new position in a straight - line fashion. This is the characteristic of a translation. There is no flipping (reflection) or turning (rotation) about a point.

Step2: Analyze second - diagram transformation

The second diagram shows a figure where the red triangle is flipped over a vertical line (the y - axis). This is the characteristic of a reflection. There is no sliding (translation) or turning (rotation) about a point.

Step3: For question 2a

First, identify the coordinates of points in $\triangle ALP$ and $\triangle A'L'P'$ by looking at the grid. Let's assume $A=(x_1,y_1)$, $L=(x_2,y_2)$, $P=(x_3,y_3)$, $A'=(x_4,y_4)$, $L'=(x_5,y_5)$, $P'=(x_6,y_6)$. For example, if $A=(2,4)$, $L=(1,2)$, $P=(3,1)$, and by observing the transformation, if $A'=( - 2,4)$, $L'=( - 1,2)$, $P'=( - 3,1)$, we can see that the x - coordinates change their signs and the y - coordinates remain the same.

Step4: For question 2b

The rule for the transformation from $(x,y)$ to $( - x,y)$ is a reflection over the y - axis.

Step5: For question 2c

To perform the transformation $(x,y)\to(x - 4,y + 1)$ on $\triangle ALP$:
For a point $(x,y)$ in $\triangle ALP$, the new x - coordinate is $x_{new}=x - 4$ and the new y - coordinate is $y_{new}=y + 1$. For example, if a point in $\triangle ALP$ is $(2,4)$, the new point after transformation is $(2-4,4 + 1)=( - 2,5)$. Plot all the new points of the transformed triangle on the grid.

Answer:

1. First diagram: Translation; Second diagram: Reflection
2. a. (Assume coordinates as per grid observation, for example) If $A=(2,4)$, $A'=( - 2,4)$; if $L=(1,2)$, $L'=( - 1,2)$; if $P=(3,1)$, $P'=( - 3,1)$

b. $(x,y)\to( - x,y)$
c. Perform $(x,y)\to(x - 4,y + 1)$ for each vertex of $\triangle ALP$ and plot the new triangle.