Question

plot the location of points a, b, and c after a translation 4 units to the right and 1 unit up. then enter the coordinates in the table. point coordinates a b c

Explanation:

1. First, assume the original coordinates of the points:

• Let's assume the coordinates of point \(A=(x_1,y_1)\), point \(B=(x_2,y_2)\), and point \(C=(x_3,y_3)\). From the graph, if we assume \(A = (- 5,5)\), \(B=(2,2)\), and \(C=(0,0)\).
• The rule for a translation \(4\) units to the right and \(1\) unit up is \((x,y)\to(x + 4,y + 1)\).

1. Calculate the new - coordinates of point \(A\):

• For point \(A\) with original coordinates \((x_1=-5,y_1 = 5)\), using the translation rule \((x,y)\to(x + 4,y + 1)\).
• The \(x\) - coordinate of \(A'\) is \(x_1+4=-5 + 4=-1\).
• The \(y\) - coordinate of \(A'\) is \(y_1+1=5 + 1 = 6\). So, the coordinates of \(A'\) are \((-1,6)\).

1. Calculate the new - coordinates of point \(B\):

• For point \(B\) with original coordinates \((x_2 = 2,y_2=2)\), using the translation rule \((x,y)\to(x + 4,y + 1)\).
• The \(x\) - coordinate of \(B'\) is \(x_2+4=2 + 4 = 6\).
• The \(y\) - coordinate of \(B'\) is \(y_2+1=2 + 1=3\). So, the coordinates of \(B'\) are \((6,3)\).

1. Calculate the new - coordinates of point \(C\):

• For point \(C\) with original coordinates \((x_3 = 0,y_3=0)\), using the translation rule \((x,y)\to(x + 4,y + 1)\).
• The \(x\) - coordinate of \(C'\) is \(x_3+4=0 + 4 = 4\).
• The \(y\) - coordinate of \(C'\) is \(y_3+1=0 + 1 = 1\). So, the coordinates of \(C'\) are \((4,1)\).

Point	Coordinates
\(B'\)	\((6,3)\)
\(C'\)	\((4,1)\)

Step1: Identify translation rule

\((x,y)\to(x + 4,y + 1)\)

Step2: Find \(A'\) coordinates

For \(A(-5,5)\), \(x=-5+4=-1,y = 5 + 1=6\)

Step3: Find \(B'\) coordinates

For \(B(2,2)\), \(x=2 + 4=6,y=2 + 1 = 3\)

Step4: Find \(C'\) coordinates

For \(C(0,0)\), \(x=0+4=4,y=0 + 1=1\)

Answer:

Point	Coordinates
\(B'\)	\((6,3)\)
\(C'\)	\((4,1)\)