Question

in the coordinate plane, the points x(11, 10), y(2, −8), and z(−7, 4) are reflected over the x-axis to the points x′, y′, and z′, respectively. what are the coordinates of x′, y′, and z′? x′ ( , ) y′ ( , ) z′ ( , )

Explanation:

Step1: Recall reflection over x - axis rule

When a point \((x,y)\) is reflected over the \(x\) - axis, the \(x\) - coordinate remains the same and the \(y\) - coordinate changes its sign. The formula for the reflection of a point \((x,y)\) over the \(x\) - axis is \((x,y)\to(x, - y)\).

Step2: Find coordinates of \(X'\)

For point \(X(11,10)\), using the reflection rule, the \(x\) - coordinate \(x = 11\) remains the same, and the \(y\) - coordinate \(y = 10\) changes to \(- 10\). So, \(X'=(11,-10)\).

Step3: Find coordinates of \(Y'\)

For point \(Y(2, - 8)\), using the reflection rule, the \(x\) - coordinate \(x = 2\) remains the same, and the \(y\) - coordinate \(y=-8\) changes to \(-(-8)=8\). So, \(Y'=(2,8)\).

Step4: Find coordinates of \(Z'\)

For point \(Z(-7,4)\), using the reflection rule, the \(x\) - coordinate \(x = - 7\) remains the same, and the \(y\) - coordinate \(y = 4\) changes to \(-4\). So, \(Z'=(-7,-4)\).

Answer:

\(X'(11, - 10)\), \(Y'(2,8)\), \(Z'(-7, - 4)\)