Question

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

Explanation:

Step1: Recall translation rule

The translation rule is \((x,y)\to(x + 2,y + 3)\).

Step2: Translate point L

For \(L(0,1)\), substitute \(x = 0\) and \(y=1\) into the rule: \(x'=0 + 2=2\), \(y'=1 + 3 = 4\). So \(L'\) is \((2,4)\).

Step3: Translate point M

For \(M(1,-2)\), substitute \(x = 1\) and \(y=-2\) into the rule: \(x'=1+ 2=3\), \(y'=-2 + 3=1\). So \(M'\) is \((3,1)\).

Step4: Translate point N

For \(N(-2,1)\), substitute \(x=-2\) and \(y = 1\) into the rule: \(x'=-2+2 = 0\), \(y'=1 + 3=4\). So \(N'\) is \((0,4)\).

Step5: Draw the original and translated triangles

On a coordinate - plane, plot the points \(L(0,1)\), \(M(1,-2)\), \(N(-2,1)\) to form the original triangle \(\triangle LMN\). Then plot the points \(L'(2,4)\), \(M'(3,1)\), \(N'(0,4)\) to form the translated triangle \(\triangle L'M'N'\).

Answer:

The coordinates of the vertices of the translated triangle are \(L'(2,4)\), \(M'(3,1)\), \(N'(0,4)\). And the original triangle with vertices \(L(0,1)\), \(M(1,-2)\), \(N(-2,1)\) and the translated triangle with vertices \(L'(2,4)\), \(M'(3,1)\), \(N'(0,4)\) should be drawn on a coordinate - plane.