Question

graph the image of δklm after a rotation 270° clockwise around the origin.

Explanation:

First, we need to identify the coordinates of the vertices of $\triangle KLM$. From the graph:

• Point $K$: Let's assume the coordinates. Looking at the grid, $K$ seems to be at $(0, -9)$ (wait, maybe I misread. Wait, the y-axis: let's check again. Wait, the points: $L$ is at $(-1, -6)$? Wait, no, the yellow points: $K$ is at $(0, -9)$? Wait, maybe better to get exact coordinates. Wait, the grid: each square is 1 unit. Let's see:

Wait, the original points:

Looking at the graph:

• Point $K$: Let's see, the vertical line (x=0) and y=-9? Wait, no, the yellow dot for K is at (0, -9)? Wait, L is at (-1, -6), M is at (1, -7)? Wait, maybe I need to re-express. Wait, the rotation rule for 270° clockwise around the origin is: $(x, y)

ightarrow (y, -x)$.

Wait, let's find the coordinates of K, L, M:

From the graph:

• $K$: Let's check the x and y. The x-coordinate: 0 (since it's on the y-axis), y-coordinate: -9? Wait, no, the grid lines: from the origin (0,0), going down, each grid is 1. So K is at (0, -9)? Wait, L is at (-1, -6) (x=-1, y=-6), M is at (1, -7) (x=1, y=-7)? Wait, maybe I made a mistake. Wait, the yellow lines: K to L is vertical? Wait, K is at (0, -9), L is at (-1, -6)? No, maybe K is at (0, -9), L is at (-1, -6), M is at (1, -7). Wait, let's confirm:

Wait, the rotation of 270° clockwise around the origin has the rule: $(x, y)
ightarrow (y, -x)$.

So let's find the original coordinates:

Looking at the graph:

• $K$: Let's see, the point K is at (0, -9) (x=0, y=-9)
• $L$: Let's see, x=-1, y=-6 (since it's 1 unit left of y-axis, 6 units down from origin)
• $M$: x=1, y=-7 (1 unit right, 7 units down)

Now apply the rotation rule $(x, y)
ightarrow (y, -x)$:

For $K(0, -9)$:

Step1: Apply rotation rule

$(0, -9)
ightarrow (-9, -0) = (-9, 0)$

For $L(-1, -6)$:

Step2: Apply rotation rule

$(-1, -6)
ightarrow (-6, -(-1)) = (-6, 1)$

For $M(1, -7)$:

Step3: Apply rotation rule

$(1, -7)
ightarrow (-7, -1)$

Now we need to plot these new points: $K'(-9, 0)$, $L'(-6, 1)$, $M'(-7, -1)$ and connect them to form the rotated triangle.

Answer:

The image of $\triangle KLM$ after a 270° clockwise rotation around the origin has vertices at $K'(-9, 0)$, $L'(-6, 1)$, and $M'(-7, -1)$. (To graph, plot these points and connect them.)