Question

translate the triangle.
then enter the new coordinates.
a(?, )
b (, )
c (, )
<3, -7>

Explanation:

Step1: Translate point A

To translate a point \((x,y)\) by the vector \(\langle a,b
angle\), we use the formula \((x + a,y + b)\). For point \(A(4,-1)\) and \(\langle3,-7
angle\), we have \(x=4,a = 3,y=-1,b=-7\). Then \(x + a=4+3\), \(y + b=-1+( - 7)\).

$$4 + 3=7$$

$$-1+( - 7)=-8$$

Step2: Translate point B

For point \(B(5,-4)\), \(x = 5,a = 3,y=-4,b=-7\). Then \(x + a=5+3\), \(y + b=-4+( - 7)\).

$$5 + 3=8$$

$$-4+( - 7)=-11$$

Step3: Translate point C

For point \(C(1,-3)\), \(x = 1,a = 3,y=-3,b=-7\). Then \(x + a=1+3\), \(y + b=-3+( - 7)\).

$$1+3 = 4$$

$$-3+( - 7)=-10$$

Answer:

\(A'(7,-8)\), \(B'(8,-11)\), \(C'(4,-10)\)