Question

which coordinate is the same as the
x - coordinate of point m?
which coordinate is the same as the
y - coordinate of point m?
opposite of x - coordinate of point m
opposite of y - coordinate of point m
y - coordinate of point m
x - coordinate of point m

Explanation:

Step1: Recall the rule for 90° clockwise rotation

When a point \((x,y)\) is rotated 90° clockwise around the origin, the new coordinates \((x',y')\) are given by \((x',y')=(y, -x)\).
For point \(M(4,3)\), after rotation, the new coordinates \(M'(3,-4)\).

Step2: Compare coordinates

• For the \(x -\)coordinate of \(M(4,3)\) and \(M'(3,-4)\): The \(x -\)coordinate of \(M\) is \(4\), and the \(x -\)coordinate of \(M'\) is \(3\) (not relevant for the answer).
• For the \(y -\)coordinate of \(M(4,3)\) and \(M'(3,-4)\): The \(y -\)coordinate of \(M\) is \(3\), and the \(y -\)coordinate of \(M'\) is \(- 4\). The \(x -\)coordinate of \(M'\) (\(3\)) is the same as the \(y -\)coordinate of \(M\) (\(3\)) before considering the sign change in the rotation formula. But when looking at the relationship between the original point \(M(4,3)\) and its rotated image \(M'(3,-4)\), the \(x -\)coordinate of \(M'\) is the \(y -\)coordinate of \(M\), and the \(y -\)coordinate of \(M'\) is the opposite of the \(x -\)coordinate of \(M\).

Answer:

The \(x -\)coordinate of \(M'\) is the \(y -\)coordinate of \(M\), and the \(y -\)coordinate of \(M'\) is the opposite of the \(x -\)coordinate of \(M\). So, for the first question (about the \(y -\)coordinate of \(M'\)), the answer is 'Opposite of \(x -\)coordinate of point \(M\)'; for the second question (about the \(x -\)coordinate of \(M'\)), the answer is '\(y -\)coordinate of point \(M\)'