Kianna lives in a town where the streets are laid out in a grid. She uses a coordinate plane to draw a map of the town, with her school at the origin. Kianna plots points for the locations of her house and her best friend Jo's house on the grid. Kianna's house is at the point (4, 2).
Kianna's and Jo's houses are reflections of each other across both axes.

1. What are the coordinates of Jo's house? Explain how you know in the space below.

2. Kianna walks from her house to Jo's house. She first walks west and then walks south. How many blocks west does Kianna walk? How many blocks south?
Write your answer in the space below.

3. Elena's house is a reflection of Jo's house across the x-axis.
What are the coordinates of Elena's house? Explain in the space below.

4. Kianna says that Elena's house is actually a reflection of her house across the y-axis.
Is Kianna right? Explain in the space below.

Whoever answers first and is right gets brainiest

1. The coordinates of Jo’s house are (-4,-2).

2. Kianna walks 8 blocks west, and 2 blocks south.

3. The coordinates of Elena’s house are (4,-2).

4. Kianna is incorrect.

Step-by-step explanation:

1. Since Jo’s house is reflected across both axes, we must reflect the coordinates two times. So we can reflect the coordinates of Kianna’s house across the x-axis first, which would give you the coordinates (4,-2). Then we reflect (4,-2) across the y axis, giving us the coordinates (-4,-2). So Jo’s house has the coordinates (-4,-2).

3. Since Elena’s house is only a reflection of Jo’s house across the x-axis only,  we can reflect Kianna’s house’s coordinates (4,2). When we reflect (4.2) over the x-axis, that gives us the coordinates (4,-2). So therefore Elena’s house has the coordinates (4,-2).

4. Kianna is incorrect, if Elena’s house was a reflection of her house across the y-axis, the coordinates would be (-4,2).

(A reflection can be thought of as folding or "flipping" an object over the line of reflection. The original object is called the pre-image, and the reflection is called the image.)

Hope this helps.

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