Question

1. a point on a coordinate grid is translated 2 units to the right and 4 units down. which rule describes this transformation?

a ((x,y)\to(2x, 4y))
b ((x,y)\to(2 + x, 4 - y))
c ((x,y)\to(x + 2, y - 4))
d ((x,y)\to(x + 2, y + 4))

Explanation:

Step1: Recall translation rules

In coordinate transformations, translating a point \((x, y)\) \(h\) units to the right and \(k\) units down means the new \(x\)-coordinate is \(x + h\) and the new \(y\)-coordinate is \(y - k\).

Step2: Apply the given translation

Here, \(h = 2\) (2 units right) and \(k = 4\) (4 units down). So the transformation rule is \((x, y)\to(x + 2, y - 4)\).

Answer:

C. \((x,y)\to(x + 2,y - 4)\)