Question

determine the coordinates for each of the following *
8 points
translation: 5 units right and 1 unit up
(2,-4) (-1,0) (-4,-2) (2,0) (0,-1) (0,-4) (-4,2) (4,0) (0,1) (-1
t
b

Explanation:

Step1: Find original coordinates

From the graph, the coordinates of point \(T\) are \((- 1,0)\) and the coordinates of point \(B\) are \((-3,-5)\).

Step2: Apply translation rule

The translation rule is \((x,y)\to(x + 5,y + 1)\).
For point \(T(-1,0)\):
Substitute \(x=-1\) and \(y = 0\) into the rule:
\(x'=-1+5=4\), \(y'=0 + 1=1\). But wait, re - check. Wait, no, if the original \(T\) is \((-1,0)\), after translation \(x=-1+5 = 4\), \(y=0 + 1=1\). Wait, no, looking at the multiple - choice, maybe there was a mis - read of original coordinates. Wait, if \(T\) is \((-1,0)\) translated \(5\) right (\(x\) becomes \(-1+5=4\)) and \(1\) up (\(y\) becomes \(0 + 1=1\)), but in the options for \(T'\) the correct is \((4,0)\)? No, wait, no, re - check. Wait, if \(T\) is \((-1,0)\), translation \((x,y)\to(x + 5,y+1)\) gives \((-1 + 5,0+1)=(4,1)\). But looking at the options for \(T'\) in the problem (maybe a mis - draw in the graph). Wait, if we assume \(T\) is \((-1,0)\) (from the position near the origin on the left - hand side), and \(B\) is \((-3,-5)\)
For \(T(-1,0)\):
\(x=-1+5 = 4\), \(y=0 + 1=1\). But in the given options for \(T'\) the user - marked is \((4,0)\) (wrong). Wait, no, re - check the translation rule. The translation is \(5\) units right (\(x\) - coordinate \(x\to x + 5\)) and \(1\) unit up (\(y\to y + 1\)).
If \(T\) is \((-1,0)\): \(T'=(-1+5,0 + 1)=(4,1)\). But in the options, maybe a typo. If we assume \(T\) is \((-1,0)\) and using the options provided (maybe the problem had \(T\) as \((-1,0)\) and \(B\) as \((-3,-5)\))
For \(B(-3,-5)\):
\(x=-3+5=2\), \(y=-5 + 1=-4\)

Answer:

\(T'=(4,1)\) (but if following the options in the problem where \(T'\) user - selected \((4,0)\) is wrong. Correct for \(B(-3,-5)\) translated \(5\) right and \(1\) up: \(B'=(2,-4)\))