Question

triangle pqr has vertices p(-2,6), q(-8,4), and r(1, -2). it is translated according to the rule (x,y)→(x - 2,y - what is the y - value of p?
-18
-16
-12
-10

Explanation:

Step1: Identify the original y - coordinate of point P

The original point \(P\) has coordinates \((-2,6)\), so the original \(y\) - value \(y_P=6\).

Step2: Apply the translation rule for the y - coordinate

The translation rule for the \(y\) - coordinate is \(y\to y - k\) (in the assumed rule \(k = 10\)). So the new \(y\) - coordinate of \(P'\) is \(y_{P'}=y_P-10\).

Step3: Calculate the new y - coordinate

Substitute \(y_P = 6\) into the formula \(y_{P'}=y_P-10\), we get \(y_{P'}=6 - 10=-4\).

Answer:

No correct option provided in the question. If the translation rule is \((x,y)\to(x - 2,y- 10)\), the y - value of \(P'\) is \(-4\). If the rule is \((x,y)\to(x - 2,y - 12)\), the y - value of \(P'\) is \(-6\) etc. Since the full translation rule \((x,y)\to(x - 2,y-\text{some value})\) is incomplete in the question, we can't get one of the given options. But if we assume the rule is \((x,y)\to(x - 2,y - 10)\):