Question

a triangle is drawn on the coordinate plane. it is translated 4 units right and 3 units down. which rule describes the translation? (x, y)→(x + 3, y - 4) (x, y)→(x + 3, y + 4) (x, y)→(x + 4, y - 3) (x, y)→(x + 4, y + 3)

Explanation:

Step1: Analyze the \(x\) - coordinate translation

When a point is translated \(a\) units to the right, the rule for the \(x\) - coordinate is \(x\to x + a\). Here, \(a = 4\) (translated 4 units right), so the \(x\) - coordinate of the point \((x,y)\) becomes \(x+4\).

Step2: Analyze the \(y\) - coordinate translation

When a point is translated \(b\) units down, the rule for the \(y\) - coordinate is \(y\to y - b\). Here, \(b = 3\) (translated 3 units down), so the \(y\) - coordinate of the point \((x,y)\) becomes \(y - 3\).

Combining these two transformations, the translation rule for the point \((x,y)\) is \((x,y)\to(x + 4,y-3)\).

Answer:

C. \((x,y)\to(x + 4,y-3)\)