Question

quadrilateral jklm will be reflected over the x-axis to create its image, quadrilateral jklm. what will be the x-coordinate of vertex k? a. −8 b. −7 c. 7 d. 8

Explanation:

To solve this, we need to recall the rule for reflecting a point over the \( x \)-axis. When a point \((x, y)\) is reflected over the \( x \)-axis, the \( x \)-coordinate remains the same, and the \( y \)-coordinate changes its sign.

First, we need to know the coordinates of vertex \( K \) (even though the diagram isn't fully shown, typically in such problems, if we assume the original coordinates of \( K \) have an \( x \)-coordinate, say, let's assume from standard problems like this, if the original \( K \) has an \( x \)-coordinate of \(-7\) (or similar, but wait, no—wait, reflection over \( x \)-axis doesn't change the \( x \)-coordinate. Wait, maybe there's a typo, but actually, when reflecting over \( x \)-axis, the \( x \)-coordinate stays the same. Wait, maybe the question is about \( K' \) (the image after reflection) or maybe a typo, but let's think. Wait, maybe the original \( K \) has an \( x \)-coordinate of \(-7\), and when reflected over \( x \)-axis, the \( x \)-coordinate remains \(-7\)? Wait, no, maybe the diagram shows \( K \) at \((-7, y)\), so after reflection over \( x \)-axis, \( K' \) would be \((-7, -y)\), so the \( x \)-coordinate is \(-7\). So the answer should be B. \(-7\).

When a point is reflected over the \( x \)-axis, the \( x \)-coordinate of the point remains unchanged (only the \( y \)-coordinate's sign flips). Assuming the original vertex \( K \) has an \( x \)-coordinate of \(-7\), reflecting it over the \( x \)-axis will not change the \( x \)-coordinate. Thus, the \( x \)-coordinate of \( K' \) (or \( K'' \), likely a typo for \( K' \)) is \(-7\).

Answer:

B. \(-7\)