Question

question 19
1 pts
what is the image of point a after a rotation of 90° in the counterclockwise direction followed by a reflection in the y-axis?
image of a coordinate grid with points g, e, d, b, f, h, c, a
options: c, g, d, h

Explanation:

Step1: Find coordinates of A

First, determine the coordinates of point \( A \). From the grid, if we assume the origin \((0,0)\) is at the center, let's find the position of \( A \). Let's count the units: moving right (x - axis) and down (y - axis). Let's say each grid square is 1 unit. So, point \( A \) has coordinates \((2, - 2)\) (since it's 2 units to the right of the y - axis and 2 units below the x - axis).

Step2: Rotate \( 90^{\circ} \) counterclockwise

The rule for a \( 90^{\circ} \) counterclockwise rotation about the origin is \((x,y)\to(-y,x)\). Applying this to \( A(2,-2) \):
\( x = 2 \), \( y=-2 \). So, after rotation, the new coordinates are \((-(-2),2)=(2,2)\).

Step3: Reflect over the y - axis

The rule for reflection over the y - axis is \((x,y)\to(-x,y)\). Applying this to the point \((2,2)\) from the previous step:
\( x = 2 \), so the new x - coordinate is \(-2\), and the y - coordinate remains 2. So the coordinates after reflection are \((-2,2)\).

Step4: Identify the point

Now, let's look at the grid. Point \( G \) has coordinates \((-2,2)\) (2 units to the left of the y - axis and 2 units above the x - axis). So the image of \( A \) after the two transformations is point \( G \).

Answer:

G