Polygon ABCD is plotted on a coordinate plane.If the polygon translates 3 units to the left and 1 unit down,the length of diagonal A’C’ is __ units ( 2,3or 6) if the polygon translates 3 units further to the left and four units down, the length of diagonal A’C’ ( increases,decreases or remains the same

The length of the diagonal will be 2.

When a translation is performed on a shaped, it simply moves location. The size and shape of the object do not change. Therefore, the length of AC will remain the same at all times.

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eudora eudora · Answer 2 · 2021-11-11T18:27:51+01:00

Length of diagonal A'C' will be 2 units and it will remain the same even after multiple translations.

Length of a segment joining two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by the expression,

Length between two points = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Therefore, length of diagonal AC joining points A(3, 4) and C(3, 2) will be,

AC = [tex]\sqrt{(3-3)^2+(4-2)^2}[/tex]

= 2 units

If the polygon ABCD is shifted left, right, up and down, translations done will be the rigid transformations showing no change in shape and size of the polygon.

Therefore, length of diagonal A'C' will be 2 units and it will remain the same when the polygon is translated.

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