Question

the point ( a(4, 1) ) is translated along the vector ( langle -5, 3
angle ) to the point ( a ). what are the coordinates of ( a )?

Explanation:

Step1: Recall translation of a point

To translate a point \((x,y)\) by a vector \(\langle a,b
angle\), we use the formula \((x + a, y + b)\). Here, the point \(A\) is \((4,1)\) and the vector is \(\langle - 5,3
angle\), so \(x = 4\), \(y=1\), \(a=-5\), \(b = 3\).

Step2: Calculate the new x - coordinate

The new \(x\) - coordinate of \(A'\) is \(x+a=4+( - 5)=4 - 5=-1\).

Step3: Calculate the new y - coordinate

The new \(y\) - coordinate of \(A'\) is \(y + b=1 + 3=4\).

Answer:

The coordinates of \(A'\) are \((-1,4)\)