Question

graph the image of v(10, -9) after a translation 3 units left and 1 unit up.

Explanation:

Step1: Recall translation rules

For a point \((x, y)\), translating \(a\) units left means subtracting \(a\) from \(x\) (since left is negative \(x\)-direction), and translating \(b\) units up means adding \(b\) to \(y\) (since up is positive \(y\)-direction). So the rule is \((x, y)\to(x - a, y + b)\) for \(a\) units left and \(b\) units up.

Step2: Apply to point \(V(10, -9)\)

Here, \(a = 3\) (left) and \(b = 1\) (up). So new \(x\)-coordinate: \(10-3 = 7\), new \(y\)-coordinate: \(-9 + 1=-8\). So the image point is \((7, -8)\). To graph, find \(x = 7\) (7 units right of origin) and \(y=-8\) (8 units down of origin) and plot the point.

Answer:

The image of \(V(10, -9)\) after translation is the point \((7, -8)\) (to graph, plot at \(x = 7\), \(y=-8\) on the coordinate plane).