Question

1. if triangle abc is reflected across the y-axis and then rotated 90 degrees clockwise, what would the coordinates of point a of the transformed triangle be? y c 2 a b 0 2 x (-2,-1) (-1,2) (-2,1) (1,2)

Explanation:

Step1: Find original coordinates of A

From the graph, point A is at \((2, 1)\) (since it's 2 units right on x - axis and 1 unit up on y - axis).

Step2: Reflect across y - axis

The rule for reflection across the y - axis is \((x,y)\to(-x,y)\). So, reflecting \((2,1)\) across the y - axis gives \((- 2,1)\).

Step3: Rotate 90 degrees clockwise

The rule for a 90 - degree clockwise rotation is \((x,y)\to(y,-x)\). Applying this to \((-2,1)\), we get \((1,2)\)? Wait, no, wait. Wait, let's re - check the rotation rule. Wait, the correct rule for 90 - degree clockwise rotation about the origin is \((x,y)\to(y, - x)\). Wait, if the pre - image after reflection is \((-2,1)\), then applying 90 - degree clockwise rotation: \(x=-2\), \(y = 1\). So the new \(x\) is \(y = 1\), the new \(y\) is \(-x=2\). Wait, that gives \((1,2)\)? But let's check the options. Wait, maybe I made a mistake in the reflection. Wait, original point A: looking at the graph, the grid lines. Let's count again. The x - coordinate of A: from the origin, moving 2 units right? Wait, no, maybe the original coordinates of A are \((2,1)\)? Wait, no, maybe I misread the graph. Wait, the triangle: point A is at (2,1)? Wait, no, looking at the graph, the x - axis has 0, 2. The y - axis has 0, 2. So point A: let's see, the horizontal line (y = 1) and vertical line (x = 2)? Wait, no, maybe the original coordinates of A are (2,1). Wait, reflection over y - axis: (2,1) becomes (-2,1). Then 90 - degree clockwise rotation: the formula for 90 - degree clockwise rotation is \((x,y)\to(y, - x)\). So substituting \(x=-2\), \(y = 1\), we get (1, 2). But (1,2) is one of the options. Wait, but let's check again. Wait, maybe the original coordinates of A are (2,1). Wait, let's confirm the rotation rule. The 90 - degree clockwise rotation about the origin: if you have a point (x,y), after 90 - degree clockwise rotation, it becomes (y, - x). So for (-2,1), x=-2, y = 1. So new x = y = 1, new y=-x = 2. So (1,2), which is option D? Wait, but let's check the options again. The options are (-2,-1), (-1,2), (-2,1), (1,2). So (1,2) is an option. Wait, but let's go through the steps again.

Wait, maybe I made a mistake in the original coordinates. Let's look at the graph again. The triangle: point A is at (2,1)? Wait, the horizontal line (y = 1) and x = 2? Then reflection over y - axis: (-2,1). Then 90 - degree clockwise rotation: (1,2). Yes, that's correct. So the final coordinates of A' are (1,2).

Answer:

(1,2)