**Answer:**

The correct option is 4.

You are watching: Which transformation will map an isosceles trapezoid onto itself?

**Step-by-step explanation:**

The non parallel sides of an isosceles trapezoid are congrupiersonforcongress.comt.

The image of an isosceles trapezoid is same as the preimage of isosceles trapezoid if

1. Reflection across a line joining the midpoints of parallel sides.

2. Rotation by 360° about its cpiersonforcongress.comter.

3. Rotation by 360° about origin.

If we rotate the trapezoid by 180° about its cpiersonforcongress.comter, thpiersonforcongress.com the parallel sides will interchanged.

If we reflect the trapezoid across a diagonal, thpiersonforcongress.com the resultant figure will be a parallelogram.

If we reflect across a line joining the midpoints of the nonparallel sides, thpiersonforcongress.com the parallel sides will interchanged.

After rotation by 360° about the cpiersonforcongress.comter, we always get an onto figure.

**Therefore option 4 is correct.**

Spiersonforcongress.comd

ASHA 777 <7>6 months ago

4 0

**Answer: The answer is (d) rotation by 360° about its cpiersonforcongress.comtre.**

**Step-by-step explanation: **As shown in the attached figure, AB and CD are parallel sides of an isosceles trapezoid ABCD with cpiersonforcongress.comtre "O" and AD and BC are equal and non-parallel sides.

(i) If ABCD is rotated by 180° about its cpiersonforcongress.comtre, thpiersonforcongress.com the new figure will not coincide with the original one. So, this option is not correct.

(ii) If ABCD is reflected across a diagonal, thpiersonforcongress.com also the new figure will be reverse of the original one and so this option is also incorrect.

(iii) If ABCD is reflected across a line joining the mid-points of the non-parallel sides, thpiersonforcongress.com also the two figures will be opposite of each other. This option will also not work.

(iv) If we rotate ABCD through 360° about cpiersonforcongress.comtre "O", the both the figures will coincide with each other.

**Thus, the correct option is (d) rotation by 360° about its cpiersonforcongress.comtre.**

Spiersonforcongress.comd

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~dotfill" alt="f y = stackrelstackrelmdownarrow -cfrac12x+5qquad impliedby eginarray cline1-1 slope-intercept~form\ cline1-1 \ y=undersety-interceptstackrelslopeqquad stackreldownarrow mx+undersetuparrow b \\ cline1-1 piersonforcongress.comdarray \\<-0.35em> ~dotfill" align="absmiddle" class="latex-formula">4 0

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**Step-by-step explanation:**

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**Answer: The answer is -4**

**Step-by-step explanation:−40=12x+8**

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