Question

△ klm has vertices k(4, −5), l(2, 2), and m(7, 3).
which translation moves the triangle so that point k lies on the y-axis?
○ a. (x, y) → (x − 4, y)
○ b. (x, y) → (x + 4, y)
○ c. (x, y) → (x, y − 5)
○ d. (x, y) → (x, y + 5)

Explanation:

Step1: Recall y - axis condition

Points on the \(y\) - axis have an \(x\) - coordinate of \(0\). The original coordinates of point \(K\) are \((4,-5)\). We need to find a translation \((x,y)\to(x + a,y + b)\) such that the new \(x\) - coordinate of \(K\) is \(0\).

Step2: Calculate the required \(x\) - translation

Let the translation for the \(x\) - coordinate be \(x\to x + a\). We want \(4 + a=0\). Solving for \(a\), we get \(a=- 4\). So the translation for the \(x\) - coordinate is \(x\to x-4\) (since \(a = - 4\)), and the \(y\) - coordinate remains unchanged ( \(b = 0\)). So the translation is \((x,y)\to(x - 4,y)\).

Answer:

A. \((x,y)\to(x - 4,y)\)