Question

which of the following shows the dilation of p (-8, 3) with a scale factor of 2?
(-16, -6)
(16, 6)
(16,- 6)
(-16, 6)

Explanation:

Step1: Recall Dilation Rule

To dilate a point \((x, y)\) with scale factor \(k\), multiply each coordinate by \(k\): \((kx, ky)\).

Step2: Apply Scale Factor

For point \(P(-8, 3)\) and \(k = 2\), calculate new \(x\)-coordinate: \(-8\times2=-16\), new \(y\)-coordinate: \(3\times2 = 6\). So the dilated point is \((-16, 6)\). Wait, no—wait, let's recheck. Wait, the options: let's recalculate. Wait, \(-8\times2=-16\), \(3\times2 = 6\), so the point is \((-16, 6)\), which is the last option. Wait, but the highlighted one was (16,6), which is wrong. Wait, no—wait, dilation about the origin? The rule is \((x,y)\to(kx,ky)\). So \(-8\times2=-16\), \(3\times2 = 6\), so \((-16, 6)\). So the correct option is the last one: \((-16, 6)\). Wait, let's check the options again. The options are:

1. \((-16, -6)\) – \(y\)-coordinate wrong (3×2=6, not -6)
2. \((16, 6)\) – \(x\)-coordinate wrong (-8×2=-16, not 16)
3. \((16, -6)\) – both wrong
4. \((-16, 6)\) – correct (x: -8×2=-16, y: 3×2=6)

So the correct answer is the fourth option: \((-16, 6)\).

Answer:

\((-16, 6)\) (the last option, \(\boldsymbol{(-16, 6)}\))