Question

the vertices of a t.ngle are ( l(0,1) ), ( m(1,-2) ), and ( n(-2,1) ). draw the figure and its image after the translation ( (x - 3,y - 4) ).

Explanation:

Step1: Find the new coordinates of point L

For point \(L(0,1)\), using the translation \((x - 3,y - 4)\):
\(x\) - coordinate: \(0-3=-3\)
\(y\) - coordinate: \(1 - 4=-3\)
New coordinates of \(L\) is \(L'(-3,-3)\)

Step2: Find the new coordinates of point M

For point \(M(1,-2)\), using the translation \((x - 3,y - 4)\):
\(x\) - coordinate: \(1-3=-2\)
\(y\) - coordinate: \(-2-4=-6\)
New coordinates of \(M\) is \(M'(-2,-6)\)

Step3: Find the new coordinates of point N

For point \(N(-2,1)\), using the translation \((x - 3,y - 4)\):
\(x\) - coordinate: \(-2-3=-5\)
\(y\) - coordinate: \(1 - 4=-3\)
New coordinates of \(N\) is \(N'(-5,-3)\)

Answer:

The vertices of the image triangle are \(L'(-3,-3)\), \(M'(-2,-6)\), and \(N'(-5,-3)\). Plot the original triangle with vertices \(L(0,1)\), \(M(1,-2)\), \(N(-2,1)\) and the translated triangle with vertices \(L'(-3,-3)\), \(M'(-2,-6)\), \(N'(-5,-3)\) on the coordinate - grid.