Question

Graph the triangle with points A(2,4) ; B(-1,3) ; C(3,1). Use the transformation given to graph the image and find the coordinates of the vertices of the images. Make sure to have 4 different graphs (1 per problem). 1. Reflection over the y-axis2. Rotation 270° clockwise about the origin3. Translation (x,y) --> (x-4,y+2) 4. Reflection over the line x = 4

Answer 1

Step-by-step explanation:

First, let's graph the initial points of the triangle A(2,4), B(-1,3), and C(3,1) as:

Then, to reflect over the y-axis, every point will be at the same distance from the y-axis but on the opposite side. It means that the graph and coordinates of the reflection are:

Where A' is located at (-2, 4), B' is located at (1, 3) and C' is located at (-3,1)

On the other hand, the coordinates of a rotation of 270° clockwise about the origin can be calculated as:

(x, y) ---> (y, -x)

A(2,4) ---> (4, -2)

B(-1,3) ----> (3, 1)

C(3,1) ----> (1, -3)

So, the graph of this transformation is:

In the same way, we can find the coordinates of the translation following the given rule:

(x,y) --> (x-4,y+2)

A(2,4) ---> (2-4, 4+2) = (-2, 6)

B(-1,3) ----> (-1-4, 3+2) = (-5, 5)

C(3,1) ----> (3-4, 1+2) = (-1, 3)

So, the graph of the translation is:

Finally, to reflect over the line x= 4 every point will be at the same distance from the x = 4 but on the opposite side. It means that the graph and coordinates of the reflection are:

Where the coordinates are A'(6, 4), B'(9, 3), and C'(5, 1)