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.

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 +2x0, -y +2y0); 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 + 21, -4 + 24) -> F (-3, 4)

I (5, 0)-> (-5 + 21, -0 + 24) -> E (-3, 8)

J (8, 0)-> (-8 + 21, -0 + 24 ) -> D (-6, 8)

deepakrai138 deepakrai138 · Answer 2 · 2021-12-23T02:41:37-05:00

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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