Question

the coordinates of the vertices of △abc are a(-2,4), b(-7,-1), and c(-3,-3). graph triangle abc and also graph its image after a translation 5 units to the right and 5 units down.

Explanation:

Step1: Plot original triangle

Plot \(A(-2,4)\), \(B(-7,-1)\), \(C(-3,-3)\) and connect.

Step2: Apply translation rule

Use \((x,y)\to(x + 5,y-5)\) for each vertex.

Step3: Calculate new coordinates for A

\(x=-2,y = 4\), \(x'=-2 + 5=3,y'=4-5=-1\) for \(A'\).

Step4: Calculate new coordinates for B

\(x=-7,y=-1\), \(x'=-7 + 5=-2,y'=-1-5=-6\) for \(B'\).

Step5: Calculate new coordinates for C

\(x=-3,y=-3\), \(x'=-3 + 5=2,y'=-3-5=-8\) for \(C'\).

Step6: Plot translated triangle

Plot \(A'(3,-1)\), \(B'(-2,-6)\), \(C'(2,-8)\) and connect.

Answer:

To graph triangle ABC:

• Plot point A(-2,4), B(-7,-1), C(-3,-3) on the coordinate - grid and connect them to form triangle ABC.

The translation rule for moving 5 units to the right and 5 units down is \((x,y)\to(x + 5,y-5)\).
For point A(-2,4):

• \(x=-2,y = 4\)
• After translation, \(x'=-2 + 5=3,y'=4-5=-1\), so the new point \(A'(3,-1)\)

For point B(-7,-1):

• \(x=-7,y=-1\)
• After translation, \(x'=-7 + 5=-2,y'=-1-5=-6\), so the new point \(B'(-2,-6)\)

For point C(-3,-3):

• \(x=-3,y=-3\)
• After translation, \(x'=-3 + 5=2,y'=-3-5=-8\), so the new point \(C'(2,-8)\)

Then plot points \(A'(3,-1)\), \(B'(-2,-6)\), \(C'(2,-8)\) on the same coordinate - grid and connect them to form the translated triangle.