Question

The point (-4, -1) is translated (x + 5, y + 2). Where is the translated point located?

Point (5, -2) is reflected across the line y = x. Where is the new location?

When figures (including points) are rotated 270° counterclockwise about the origin, it is also the same rotating figures clockwise by what other degree amount?

Triangle ABC is located at A(-4,5), B (-4, -1), and C(-1,1). A translation of the triangle is located at A’(-7, 3), B’(-7, -3), and C’(-4, -1). How is the triangle translated?

Triangle ABC is translated 3 units left and 2 units down.
Triangle ABC is translated 2 units left and 3 units down.
Triangle ABC is translated 2 units right and 3 units up.
Triangle ABC is translated 3 units right and 2 units up.

Quadrilateral WXYZ is located at W(2,1), X(5,2), Y(4, 4), Z(2,4). A translation of the quadrilateral is located at W’(-2, -2), X’(1, -1), Y’(0, 1), Z’(-2, 1). How is the quadrilateral translated?

Quadrilateral WXYZ is translated 3 units to the right and 4 units up.
Quadrilateral WXYZ is translated 4 units to the right and 3 units up.
Quadrilateral WXYZ is translated 3 units to the left and 3 units down.
Quadrilateral WXYZ is translated 4 units to the left and 3 units down.

Answer 1

Triangle ABC is translated 2 units left and 3 units down.
Quadrilateral WXYZ is translated 4 units to the left and 3 units down.

Answer 2

1. The new point is located at (1,1).
Because the point is translated x + 5, y + 2, we need to add these values to the x and y coordinates.
(-4,-1) - x = -4, y = -1
-4 + 5 = 1
-1 + 2 = 1
Therefore, the new coordinates are (1,1).

2. The new point is located at (-2,5).
When reflecting across the line y = x, all you have to do is switch y and x. This is because the line y = x is a diagonal line that goes up and to the right through the origin, so, when a point is reflected across it, it goes into the opposite quadrant. The reason y = x is a diagonal line is because the y value is the same as the x value, meaning that the points are all along the lines of (1,1), (2,2), or (1/2,1/2).
(5,-2) = (-2,5)
Therefore, the new coordinates are (-2,5).

3.The figure would have to be rotated clockwise 90°.
If the figure is rotated counterclockwise 270°, that means that it is now 90° away from its original position. This is because a figure can rotate a total of 360°, meaning that after rotating a figure counterclockwise 270°, it is 90° away from its initial position.
360 - 270 = 90
Therefore, the figure would have to be rotated clockwise 90°.

4. Triangle ABC is translated 3 units left and 2 units down.
We can find out how many units the figure moved each time by subtracting the original coordinates from the new coordinates.
(-7,3) = (-4,5)
-7 - -4 = -3
3 - 5 = -2
The x coordinate moved 3 units left and the y coordinate moved 2 units down.
(-7,-3) = (-4,-1)
-7 - -4 = -3
(-3 - -1) = -2
The x coordinate moved 3 units left and the y coordinate moved 2 units down.
(-4,-1) = (-1,1)
-4 - -1 = -3
-1 - 1 = -2
The x coordinate moved 3 units left and the y coordinate moved 2 units down.
Therefore, each point moved left 3 units and down 2 units.

5. Quadrilateral WXYZ is translated 4 units to the left and 3 units down.
(-2,-2) = (2,1)
-2 - 2 = -4
-2 - 1 = -3
The x coordinate moved 4 units left and the y coordinate moved 3 units down.
(1,-1) = (5,2)
1 - 5 = -4
-1 - 2 = -3
The x coordinate moved 4 units left and the y coordinate moved 3 units down.
(0,1) = (4,4)
0 - 4 = -4
1 - 4 = -3
The x coordinate moved 4 units left and the y coordinate moved 3 units down.
(-2,1) = (2,4)
-2 - 2 = -4
1 - 4 = -3
The x coordinate moved 4 units left and the y coordinate moved 3 units down.
Therefore, each point moved 4 units left and 3 units down.

Hope this helps!