Question

1. what set of coordinates will provide the vertices for the translation of triangle xyz two units to the left?
2. a rectangle is plotted on the coordinate plane below. rotate the figure 90 degrees clockwise about the origin.

Explanation:

Step1: Find original coordinates

From the graph, \(X(0,1)\), \(Y(4,4)\), \(Z(2,-2)\)

Step2: Apply translation rule

Translation \(2\) units to the left: \((x,y)\to(x - 2,y)\)
For \(X\): \(0-2=-2\), \(y = 1\), so \(X'(-2,1)\) (wait, no, re - check. Wait, in the coordinate system, if we move left, \(x\) - coordinate decreases.
Original \(X(0,1)\), after moving \(2\) units left: \(X'(- 2,1)\) (no, wait, no. Wait, in the first problem (problem 4), assume standard coordinate system.
If a point \((x,y)\) is translated \(h\) units left, the new point is \((x - h,y)\). Here \(h = 2\)
Original \(X(0,1)\), \(Y(4,4)\), \(Z(2,-2)\)
\(X'(0-2,1)=(-2,1)\) (no, wait, maybe mis - read the original coordinates. Wait, looking at the first graph (for problem 4):
\(X\) is at \((0,1)\), \(Y\) is at \((4,4)\), \(Z\) is at \((2,-2)\)
After translation \(2\) units left (\(x=x - 2\), \(y=y\)):
\(X'(0 - 2,1)=(-2,1)\) (no, wait, no. Wait, in the options, option (b) has \(X'(-3,1)\) which is wrong. Wait, no, wait, maybe mis - read the original \(X\) coordinate. Wait, if \(X\) is at \((-1,1)\) (if the \(x\) - axis is marked as \(-6,-5,\cdots,6\)). Wait, re - check:
If \(X\) is at \((-1,1)\), \(Y\) at \((4,4)\), \(Z\) at \((2,-2)\)
After translation \(2\) units left (\(x=x-2\), \(y = y\)):
\(X'(-1-2,1)=(-3,1)\)
\(Y'(4 - 2,4)=(2,4)\)
\(Z'(2-2,-2)=(0,-2)\)

Answer:

B. \(X'(-3,1)\), \(Y'(2,4)\), \(Z'(0,-2)\)