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Help please i dont understand

Help please i dont understand-example-1
User Martino
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1 Answer

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Explanation:

if 2 shapes are truly congruent, then after some turning and rotating they can cover each other up completely with no spot being uncovered, nothing "hangs over".

now, if one shape is a larger version of the other, then this is violated, of course. they cannot be congruent.

in our case here the " version is made 4 times as large as the original. so, no congruence, abd the 3rd answer option is already disqualified.

a dilation scale factor 4 means the new parallelogram is the old parallelogram multiplied by 4.

A"B"C"D" is the new one.

let's use point A (3, 3) as example.

since the center of the dilation is the origin, the scaling simply multiplied the coordinates by the scaling factor.

A' = A × 4 = (3×4, 3×4) = (12, 12)

the following reflection across the y-axis keeps the y- values.

so, A" has the same y-value as A' = 12.

therefore, the 1st and the 4th answer options are wrong too.

the remaining (and correct) answer option is the 2nd.

just to check : all coordinates are multiplied by 4 due to the dilation, and the x-values are +/- reversed due to the reflection across the y-axis (and the y- values are kept the same).

(3, 3) -> (12, 12) -> (-12, 12)

(-1, 3) -> (-4, 12) -> (4, 12)

(-4, 1) -> (-16, 4) -> (16, 4)

(0, 1) -> (0, 4) -> (0, 4)

and again, a blown up version of the original shape has still the same proportions (so they are similar) but not the same size (no congruence).

User Chapsterj
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