Question

point a, located at $(-11, -7)$ on the coordinate plane, is reflected over the $x$-axis to form point b. then point b is reflected over the $y$-axis to form point c. what are the coordinates of points b and c? point b: $(-11,7)$ point c: $(11,7)$; point b: $(11, -7)$ point c: $(-11,7)$; point b: $(11, -7)$ point c: $(11,7)$; point b: $(-11,7)$ point c: $(11, -7)$

Explanation:

Step1: Reflect over x - axis

To reflect a point \((x,y)\) over the \(x\) - axis, the rule is \((x,y)\to(x, - y)\). For point \(A(-11,-7)\), when we reflect it over the \(x\) - axis to get point \(B\), we keep the \(x\) - coordinate the same and change the sign of the \(y\) - coordinate. So \(x=-11\) and \(y = -(-7)=7\). Thus, the coordinates of \(B\) are \((-11,7)\).

Step2: Reflect over y - axis

To reflect a point \((x,y)\) over the \(y\) - axis, the rule is \((x,y)\to(-x,y)\). For point \(B(-11,7)\), when we reflect it over the \(y\) - axis to get point \(C\), we change the sign of the \(x\) - coordinate and keep the \(y\) - coordinate the same. So \(x=-(-11) = 11\) and \(y = 7\). Thus, the coordinates of \(C\) are \((11,7)\).

Answer:

Point \(B\): \((-11,7)\)
Point \(C\): \((11,7)\) (corresponding to the first option: Point \(B\): \((-11,7)\); Point \(C\): \((11,7)\))