Which transformation will map an isosceles trapezoid onto itself? rotation by 180° about its center, reflection across a diagonal, reflection across a line joining the midpoints of the nonparallel sides, rotation by 360° about its center

The correct option is 4.

Step-by-step explanation:

The non parallel sides of an isosceles trapezoid are congruent.

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 center.

3. Rotation by 360° about origin.

If we rotate the trapezoid by 180° about its center, then the parallel sides will interchanged.

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

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

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

Therefore option 4 is correct.

The answer is (d) rotation by 360° about its centre.

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

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

(ii) If ABCD is reflected across a diagonal, then 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, then also the two figures will be opposite of each other. This option will also not work.

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

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

answer: e 9, 5.75

step-by-step explanation:

step 1

find the variation ab in the x coordinate

delta x=(x2-x1)=10-> 8 units

find the variation ab  in the y coordinate 

delta y=(y2-y1)=6-> 2 units

step 2

find the coordinates point c

  x coordinate 

cx=ax+delta x*2/> cx=2+8*(2/> cx=3

  y coordinate 

cy=ay+delta y*2/> cy=4+2*(2/> cy=4.25

the coordinates of point c are (3,4.25)

step 3

find the coordinates point d

  x  coordinate 

dx=ax+delta x*4/> dx=2+8*(4/> dx=4

  y  coordinate 

dy=ay+delta y*4/> dy=4+2*(4/> dy=4.5

the coordinates of point d are (4, 4.5)

step 4

find the coordinates point e

  x  coordinate 

ex=ax+delta x*4/> ex=2+8*(6/> ex=5

  y  coordinate 

ey=ay+delta y*4/> ey=4+2*(6/> ey=4.75

the coordinates of point e are (5, 4.75)

step 5

find the coordinates point f

  x  coordinate 

fx=ax+delta x*4/> fx=2+8*(8/> fx=6

  y  coordinate 

fy=ay+delta y*4/> fy=4+2*(8/> fy=5

the coordinates of point f are (6,5)

step 6

find the coordinates point g

  x  coordinate 

gx=ax+delta x*4/> gx=2+8*(10/> gx=7

  y  coordinate 

gy=ay+delta y*4/> gy=4+2*(10/> gy=5.25

the coordinates of point g are (7,5.25)

step 7

find the coordinates point h

  x  coordinate 

hx=ax+delta x*4/> hx=2+8*(12/> hx=8

  y  coordinate 

hy=ay+delta y*4/> hy=4+2*(12/> hy=5.5

the coordinates of point h are (8,5.5)

step 8

find the coordinates point i

  x  coordinate 

ix=ax+delta x*4/> ix=2+8*(14/> ix=9

  y  coordinate 

iy=ay+delta y*4/> iy=4+2*(14/> iy=5.75

the coordinates of point i are (9,5.75)

- r3ktforgood ☕

answer: median

step-by-step explanation:

the median is the middle value when a data set is ordered from least to greatest