1. A point A(7,2) is rotated counterclockwise about the origin by 90' and its image is then translated down 2 units. If the final point is labeled as A" then which of the following would be the length of AA"?

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1 A point A72 is rotated counterclockwise about the origin by 90 and its image is then translated down 2 units If the final point is labeled as A then which of class=

Respuesta :

Answer: (2) Square root of 90

Step-by-step explanation:

After you rotate it counterclockwise around the origin by 90 degrees, the point would be (-2,7). Since you translate it down by 2, it would then be (-2,5). The points (-2,5) and the original point (7,2) would form the hypotenuse of a right triangle and you can use the Pythagorean Theorem to find the length of the hypotenuse. The length is 9 units, the height is 3 units.

[tex]3^2+9^2=c^2\\ 9+81=c^2\\ 90=c^2\\ \sqrt{90}=c[/tex]