Graph △XYZ with vertices X(2, 3), Y(−3, 2), and Z(−4,−3) and its image after the translation (x, y)→(x+3, y−1).

Question

Graph △XYZ with vertices X(2, 3), Y(−3, 2), and Z(−4,−3) and its image after the translation (x, y)→(x+3, y−1).

What are the coordinates for triangle XYZ after the translation?

Please show all the work on how you got your answers.

Answer 1

To find the coordinates of triangle XYZ after the translation, we need to apply the given translation to each vertex of the triangle.

Let's start with the vertex X(2, 3).

For the vertex X, the x-coordinate will be increased by 3, and the y-coordinate will be decreased by 1.

So the new coordinates for X after the translation are:
X'(2 + 3, 3 - 1) = X'(5, 2)

Now, let's move to the vertex Y(-3, 2).

For the vertex Y, the x-coordinate will be increased by 3, and the y-coordinate will be decreased by 1.

So the new coordinates for Y after the translation are:
Y'(-3 + 3, 2 - 1) = Y'(0, 1)

Finally, let's move to the vertex Z(-4, -3).

For the vertex Z, the x-coordinate will be increased by 3, and the y-coordinate will be decreased by 1.

So the new coordinates for Z after the translation are:
Z'(-4 + 3, -3 - 1) = Z'(-1, -4)

Therefore, the coordinates for triangle XYZ after the translation are:
X'(5, 2), Y'(0, 1), and Z'(-1, -4).

So the translated triangle XYZ has its vertices at X'(5, 2), Y'(0, 1), and Z'(-1, -4).

Answer 2

To find the coordinates of triangle XYZ after the translation, we need to apply the given translation rule (x, y) → (x + 3, y - 1) to each vertex of the original triangle.

Let's start by finding the coordinates of the translated vertex X':

x' = x + 3
y' = y - 1

For the vertex X(2, 3), substitute x = 2 and y = 3 into the translation rule:

x' = 2 + 3
y' = 3 - 1

x' = 5
y' = 2

So, the coordinates for the translated vertex X' are (5, 2).

Next, let's find the coordinates of the translated vertex Y':

x' = x + 3
y' = y - 1

For the vertex Y(-3, 2), substitute x = -3 and y = 2 into the translation rule:

x' = -3 + 3
y' = 2 - 1

x' = 0
y' = 1

So, the coordinates for the translated vertex Y' are (0, 1).

Finally, let's find the coordinates of the translated vertex Z':

x' = x + 3
y' = y - 1

For the vertex Z(-4, -3), substitute x = -4 and y = -3 into the translation rule:

x' = -4 + 3
y' = -3 - 1

x' = -1
y' = -4

So, the coordinates for the translated vertex Z' are (-1, -4).

Therefore, the coordinates for triangle XYZ after the translation are:
X'(5, 2)
Y'(0, 1)
Z'(-1, -4)

Answer 3

Let's look at the first coordinate

(2,3) you will need to add 3 to the x coordinat (2 + 3)
and subtract 1 from the y coordinate (3-1)
(2+3, 3 -1)
So (2,3) became (5, 2)
Now you do the other 2 vertices : )