Question

symmetry on the coordinate plane
find the equations of lines of symmetry. select all that apply.
y = 4
x = 4
x - axis
none
y - axis

Explanation:

Step1: Recall line - symmetry concept

A line of symmetry divides a figure into two congruent parts such that one part is the mirror - image of the other. For a triangle on the coordinate plane, we check each option.

Step2: Analyze \(y = 4\)

If we consider the line \(y = 4\), the triangle is not symmetric about this line as the parts above and below \(y = 4\) are not mirror - images.

Step3: Analyze \(x = 4\)

The line \(x = 4\) passes through the vertex \(B\) and is the perpendicular bisector of the base \(AC\). Reflecting the triangle across \(x = 4\) will result in the triangle overlapping itself. So \(x = 4\) is a line of symmetry.

Step4: Analyze \(x\) - axis

Reflecting the triangle across the \(x\) - axis will not result in the triangle overlapping itself as the vertices above and below the \(x\) - axis are not arranged symmetrically with respect to the \(x\) - axis.

Step5: Analyze \(y\) - axis

Reflecting the triangle across the \(y\) - axis will not result in the triangle overlapping itself as the vertices to the left and right of the \(y\) - axis are not arranged symmetrically with respect to the \(y\) - axis.

Answer:

x = 4