Triangle RST and its image, triangle R’S’T’, are graphed on the coordinate grid below. On a coordinate plane, triangle R S T has points (0, 1), (negative 2, 2), (negative 1, 4). Triangle R prime S prime T prime has points (1, 0), (2, 2), (4, 1). Which rotation, using the origin as the center of rotation, transformed RST to R’S’T’? a 90° clockwise rotation a 90° counterclockwise rotation a 45° clockwise rotation a 45° counterclockwise rotation

Given:

The coordinates of the triangle RST are (0,1), (-2,2) and (-1,4)

The coordinates of the triangle R'S'T' are (1,0), (2,2) and (4,1)

We need to determine the rotation about origin.

Rotation about the origin:

To determine the rotation about the origin, we need to find the translation rule.

The coordinates of the point R to R' is

The translation rule for the point R to R' is

The coordinate of the point S to S'is

The translation rule for the point S to S' is

The coordinates of the point T to T' is

The translation rule for the point T to T' is

Therefore the rule to translate the triangle RST to R'S'T' is

Hence, the triangle is rotated 90° clockwise about the origin.

Hence, Option a is the correct answer.

d) 30 units^2

area of rectangle = l × b

we know,

length = 10 unit

breadth = 3 unit

applying the formula,

= l × b

= 10 × 3

= 30 unit^2

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