Question

write the coordinates of the vertices after a translation 10 units left and 5 units up.

Explanation:

Step1: Identify original coordinates

From the graph, we find the original coordinates:

• \( P(8, -6) \)
• \( Q(8, 3) \) (assuming the y - coordinate of Q is 3, as it is 3 units above the x - axis at x = 8)
• \( R(2, -5) \) (assuming the y - coordinate of R is - 5, as it is 5 units below the x - axis at x = 2)

Step2: Apply translation rules

The translation rule for a point \((x,y)\) moved \(a\) units left (so \(x\) becomes \(x - a\)) and \(b\) units up (so \(y\) becomes \(y + b\)) is \((x,y)\to(x - 10,y + 5)\) (since \(a = 10\) and \(b = 5\)).

For point \(P(8,-6)\):

New \(x\) - coordinate: \(8-10=-2\)
New \(y\) - coordinate: \(-6 + 5=-1\)
So \(P'\) is \((-2,-1)\)

For point \(Q(8,3)\):

New \(x\) - coordinate: \(8-10=-2\)
New \(y\) - coordinate: \(3 + 5 = 8\)
So \(Q'\) is \((-2,8)\)

For point \(R(2,-5)\):

New \(x\) - coordinate: \(2-10=-8\)
New \(y\) - coordinate: \(-5 + 5=0\)
So \(R'\) is \((-8,0)\)

Answer:

The coordinates of the vertices after translation are \(P'(-2,-1)\), \(Q'(-2,8)\), \(R'(-8,0)\)