Question

A coordinate plane shows the x and y axes ranging from negative 5 to 5 in increments of 1. A drawing of a house is shown on quadrant 2. The apex of the house is marked at the joining of the two slanting lines of the roof. The coordinates of the apex is point upper A left parenthesis negative 3 start fraction 1 over 2 end fraction comma 4 right parenthesis. There is an entrance, two windows, and a chimney on the right side of the house.
If the image of the house is reflected across the x
-axis, what will the coordinates of A′
be? (1 point)
Responses

(4,−312)
left parenthesis 4 comma negative 3 Start Fraction 1 over 2 End Fraction right parenthesis

(−312,−4)
left parenthesis negative 3 Start Fraction 1 over 2 End Fraction comma negative 4 right parenthesis

(312,4)
left parenthesis 3 Start Fraction 1 over 2 End Fraction comma 4 right parenthesis

(312,−4)

Answer 1

When reflecting a point across the x-axis, the x-coordinate remains the same while the y-coordinate changes its sign.

Given the coordinates of point A as \((-3 \frac{1}{2}, 4)\), we can write this in improper fraction form for clarity:

\[-3 \frac{1}{2} = -\frac{7}{2}\]

Now, reflecting across the x-axis means we keep the x-coordinate and change the y-coordinate from \(4\) to \(-4\):

Thus, \(A' = \left(-3 \frac{1}{2}, -4\right)\).

Therefore, the correct response is:
\[
\left(-3 \frac{1}{2}, -4\right)
\]