Question

question #2: dilate the point g(84, 35) by a scale factor of 1/7 and reflect across the line y = -x. (y, -x)

Explanation:

Step1: Dilate the point G(84, 35) by scale factor 1/7

To dilate a point \((x, y)\) by a scale factor \(k\), we use the formula \((kx, ky)\). Here, \(x = 84\), \(y = 35\), and \(k=\frac{1}{7}\).

For the \(x\)-coordinate: \(84\times\frac{1}{7}=12\)

For the \(y\)-coordinate: \(35\times\frac{1}{7} = 5\)

So the dilated point is \((12, 5)\).

Step2: Reflect the dilated point across the line \(y=-x\)

The rule for reflecting a point \((a, b)\) across the line \(y = -x\) is \((-b, -a)\).

For the point \((12, 5)\), \(a = 12\) and \(b = 5\).

Applying the rule: \((-5, -12)\)

Answer:

\((-5, -12)\)