Question

the vertices of △def are located at d(5/8, -2), e(4, 3), and f(-3/2, 7/4). △def is reflected across the x - axis to form △def. what are the coordinates of △def? how can the transformation that maps △def to △def be described algebraically? fill in the blanks to complete the statements. the vertices of △def are d(5/8, 2), e□, and f□. the transformation can be described algebraically as (x, y)→(x, - y).

Explanation:

Step1: Reflect point \(E(4,3)\) across the \(x -\)axis

When reflecting a point \((x,y)\) across the \(x -\)axis, the \(x -\)coordinate remains the same and the \(y -\)coordinate changes its sign. For point \(E(4,3)\), using the rule \((x,y)\to(x, - y)\), we get \(E'(4,-3)\)

Step2: Reflect point \(F(-\frac{3}{2},\frac{7}{4})\) across the \(x -\)axis

For point \(F(-\frac{3}{2},\frac{7}{4})\), applying the rule \((x,y)\to(x, - y)\), we change the sign of the \(y -\)coordinate. So \(F'(-\frac{3}{2},-\frac{7}{4})\)

Answer:

\(E'=(4, - 3)\), \(F'=(-\frac{3}{2},-\frac{7}{4})\)