Question

Rectangle stuv is shown on a coordinate plane. rectangle stuv with vertices s at negative 7 comma 6, t at negative 2 comma 6, u at negative 2 comma 1, and v at negative 7 comma 1. if rectangle stuv is translated using the rule (x, y) ? (x ? 2, y ? 4) and then rotated 90� counterclockwise, what is the location of v?? (3, ?9) (3, ?4) (?2, ?4) (?2, ?9)

Answer 1

The location of point V after the translation and rotation is (3, -9).

Step-by-step explanation:

The rectangle STUV is translated 2 units left and 4 units down, resulting in the coordinates:

S: (-7, 6) ? (-9, 2)

T: (-2, 6) ? (-4, 2)

U: (-2, 1) ? (-4, -3)

V: (-7, 1) ? (-9, -3)

Next, the rectangle is rotated 90° counterclockwise. To rotate a point (x, y) 90° counterclockwise, the new coordinates are (-y, x). Applying this to the point V (-9, -3), we get:

V' = (-(-3), -9) = (3, -9)

Therefore, the location of point V after the translation and rotation is (3, -9).

Answer 2

If rectangle STUV is translated using the rule (x, y) → (x − 2, y − 4) and then rotated 90° counterclockwise, the location of V″ is: A. (3, -9).

In Mathematics, a translation is a type of transformation that shifts every point of a geometric object in the same direction on the cartesian coordinate, as well as for the same distance.

In this exercise, we would apply a translation 2 units to the left and 4 units down to rrectangle STUV, in order to determine the coordinates of its image as follows;

(x, y) → (x - 2, y - 4)

V (-7, 1) → (-7 - 2, 1 - 4) = V' (-9, -3).

Next, we would apply a rotation of 90° counterclockwise to the new coordinates of V as follows;

(x, y) → (-y, x)

V (-9, -3) → V" (3, -9).

Complete Question:

Rectangle STUV is shown on a coordinate plane.

If rectangle STUV is translated using the rule (x, y) → (x − 2, y − 4) and then rotated 90° counterclockwise, what is the location of V″?

(3, -9)

(3, -4)

(-2, -4)

(-2, -9)