izzybelle3
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sumy is working in geometry class and it's given figure ABCD in the coordinate plane to reflect. the coordinates of Point D are (a, b) and she reflects a figure over the line Y equals X. What are the coordinates of the image d?

A. (a,-b)

B. (b, a)

c. (-a, b)

D. (-b,-a)

Respuesta :

frika
If point D with coordinates (a,b) is reflected over the line y=x then the image point D' coordinates are (b,a) (see picture for details). 

The middlepoint M of segment DD' lhas coordinates [tex]( \frac{a+b}{2} , \frac{b+a}{2} )[/tex] and lies on the line y=x (since its coordinates are equal), DD' is perpendicular to the line y=x and DM=D'M. All these remarks show that the point D' is the image point of D.

Answer: Correct choice is B.

Ver imagen frika

The image of the point D following a reflection across the line y = x reverses

the positions of the x and y-values in the ordered pair.

The coordinates of the image, d, is [tex]\underline{B. \ (b, \, a)}[/tex]

Reasons:

The reflection of a point (x, y) over the line y = x, gives the image of the

preimage at the point (y, x).

Therefore, the location of the image of the point D(a, b) following a

reflection across the line y = x is the point d(b, a)

D(a, b) [tex]\underrightarrow {r_{y = x}}[/tex] d(b, a)

The correct option is B.  [tex]\underline{ (b, \, a)}[/tex]

Learn more here:

https://brainly.com/question/19517048

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