Question

day 5a check in which type of transformation is pictured below? show how you know!
the figure ______ rotated about the origin. degrees counterclockwise / clockwise
success criteria
i can determine which shape is the preimage and which is the image.
i can explain the 90 rotation (clockwise or counterclockwise) that occurred to take the one figure to its image in words.
i can explain the properties that are preserved and not preserved under a rotation.
mastery level
name

Explanation:

Step1: Identify the transformation type

Rotation is a transformation that turns a figure around a fixed point (the origin in this case).

Step2: Determine the rotation direction

By observing the orientation of the figure, it is rotating in the clockwise direction.

Step3: Calculate the rotation degree

We can use the properties of coordinate rotation. For a point \((x,y)\) rotated \(90^{\circ}\) clockwise about the origin, the new coordinates \((x',y')=(y, -x)\).
Let's take a point from the pre - image triangle \(F(-4,-2)\), \(G(-2,-2)\), \(H(-3,1)\) and its image \(F'( - 2,-4)\), \(G'(2,-2)\), \(H'(1,-3)\).
For point \(H(-3,1)\), if we rotate it \(90^{\circ}\) clockwise about the origin: using the formula \((x,y)\to(y, -x)\), we get \((1,3)\) (wait, no, let's re - check.
Another way: count the angle between the corresponding sides of the pre - image and image. The angle between the sides of the two triangles is \(90^{\circ}\).

Answer:

The figure is rotated \(90\) degrees clockwise about the origin.