Question

Identify JIG --->DEF as a reflection, translation, rotation, or glide reflection. Find the reflection line, translation rule, center and angle of rotation, or glide translation rule and reflection line.

Answer 1

Answer:

rotation 180° about (1, 4)

Step-by-step explanation:

When rotation is made about origin, i. e., point (0, 0); points of the shape transform from (x, y) to (-x, -y). But when the rotation is about point (x0,  y0) the points transform from (x, y) to (-x +2*x0, -y +2*y0); notice that rotation about origin is a special case of this more general rule.

Then, the transformations about point (1, 4) are:

G (5, 4)-> (-5 + 2*1, -4 + 2*4) -> F (-3, 4)

I (5, 0)-> (-5 + 2*1, -0 + 2*4) -> E (-3, 8)

J (8, 0)-> (-8 + 2*1, -0 + 2*4 ) -> D (-6, 8)

Answer 2

Rotation 180° about (1, 4).

When rotation is made about origin(0, 0) the coordinates transform from (x, y) to (-x, -y). But when the rotation is about point ($x_{0}$, $y_{0}$) the points transform from (x, y) to ($-x +2\times x_{0}$, $-y +2\times y_{0}$).

Now, the transformations about point (1, 4) are:

G (5, 4) is ($-5 + 2\times 1$, $-4 + 2\times 4$) or F (-3, 4)

I (5, 0) is ($-5 + 2\times 1$, $-0 + 2\times 4$) or E (-3, 8)

J (8, 0) is (-$8 + 2\times 1$, $-0 + 2\times 4$ ) or D (-6, 8)

Hence JIG --->DEF is a Rotation about (1, 4).

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