Question

michael draws △pqr on a coordinate plane, as shown.
michael reflects △pqr across the x - axis to form △pqr and then across the y - axis to form △pqr.
what are the coordinates of vertex q?
q (□,□)

Explanation:

Step1: Find the coordinates of point \( Q \)

Assume the coordinates of \( Q \) are \( (x,y) \). From the graph (assuming standard grid - based coordinate system), if we count the units, let's say \( Q=(6,1) \) (the exact coordinates depend on the graph's scale. But for reflection rules:

• Reflection across the \( x \) - axis: The rule is \( (a,b)\to(a, - b) \). So if \( Q=(6,1) \), after reflection across the \( x \) - axis, \( Q'=(6, - 1) \).
• Reflection across the \( y \) - axis: The rule is \( (a,b)\to(-a,b) \).

Step2: Apply double - reflection (first \( x \) - axis then \( y \) - axis)

If we first reflect \( Q=(6,1) \) across the \( x \) - axis to get \( Q'=(6, - 1) \), then reflect \( Q'=(6, - 1) \) across the \( y \) - axis. Using the rule \( (a,b)\to(-a,b) \), we substitute \( a = 6 \) and \( b=-1 \). So \( Q''=(-6,-1) \)

Answer:

\((-6,-1)\)