Question

1. transform the figure using the sequence of transformation: (x,y)→(y+1,1−x)

Explanation:

Step1: Identify Original Coordinates

First, find the coordinates of points A, B, and C from the graph.

• Point A: Let's assume from the grid, A is at \((-4, 1)\) (since it's 4 units left on x - axis and 1 unit up on y - axis).
• Point B: B is at \((-4, -1)\) (4 units left on x - axis and 1 unit down on y - axis).
• Point C: C is at \((-2, -1)\) (2 units left on x - axis and 1 unit down on y - axis).

Step2: Apply Transformation \((x,y)\to(y + 1,1 - x)\) to Each Point

For Point A \((-4,1)\):

Substitute \(x=-4\) and \(y = 1\) into the transformation formula.
New \(x\) - coordinate: \(y+1=1 + 1=2\)
New \(y\) - coordinate: \(1-x=1-(-4)=1 + 4 = 5\)
So, the image of A, say \(A'\), is \((2,5)\).

For Point B \((-4,-1)\):

Substitute \(x = - 4\) and \(y=-1\) into the transformation formula.
New \(x\) - coordinate: \(y + 1=-1+1 = 0\)
New \(y\) - coordinate: \(1-x=1-(-4)=5\)
So, the image of B, say \(B'\), is \((0,5)\).

For Point C \((-2,-1)\):

Substitute \(x=-2\) and \(y = - 1\) into the transformation formula.
New \(x\) - coordinate: \(y+1=-1 + 1=0\)
New \(y\) - coordinate: \(1-x=1-(-2)=3\)
So, the image of C, say \(C'\), is \((0,3)\).

Step3: Plot the Transformed Points

Plot the points \(A'(2,5)\), \(B'(0,5)\), and \(C'(0,3)\) on the coordinate grid and connect them to get the transformed figure.

Answer:

The transformed figure has vertices at \(A'(2,5)\), \(B'(0,5)\), and \(C'(0,3)\) (and the figure is a triangle formed by these three points). To visualize, plot these points on the given grid and draw the lines between them.