Question

1. what is the result of translating the point (3, 4) according to ( t_{7,-5} )?

(10, 1)
(10, -1)
(7, -5)
(7, 1)

Explanation:

Step1: Understand the translation rule

The translation \(T_{a,b}\) means adding \(a\) to the \(x -\)coordinate and \(b\) to the \(y -\)coordinate of a point \((x,y)\). Here \(a = 7\) and \(b=-5\), and the original point is \((x,y)=(3,4)\).

Step2: Calculate the new \(x -\)coordinate

For the \(x -\)coordinate: \(x'=x + a\). Substitute \(x = 3\) and \(a = 7\) into the formula. Then \(x'=3 + 7=10\).

Step3: Calculate the new \(y -\)coordinate

For the \(y -\)coordinate: \(y'=y + b\). Substitute \(y = 4\) and \(b=-5\) into the formula. Then \(y'=4+( - 5)=4 - 5=-1\).

Answer:

\((10,-1)\)