Question

if the triangle on the grid below is translated by using the rule $(x,y)\to(x + 5,y - 2)$, what will be the coordinates of $b$?
$(-2,0)$
$(0,-2)$
$(5,-7)$
$(5,-2)$

Explanation:

Step1: Find the original coordinates of point B

From the grid, the coordinates of point B are \((-5, 2)\).

Step2: Apply the translation rule \((x,y)\to(x + 5,y-2)\)

For the \(x\)-coordinate: \(x=-5\), after translation \(x'=-5 + 5=0\).
For the \(y\)-coordinate: \(y = 2\), after translation \(y'=2-2 = 0\).

Answer:

\((0,0)\)

Wait, there seems to be a mistake. Let's re - check.

Step1: Re - find the original coordinates of point B

Looking at the grid again, point B is at \((-5,0)\) (since it's on the \(x\) - axis where \(y = 0\)).

Step2: Apply the translation rule \((x,y)\to(x + 5,y-2)\)

For the \(x\) - coordinate: \(x=-5\), after translation \(x'=-5 + 5=0\).
For the \(y\) - coordinate: \(y = 0\), after translation \(y'=0-2=-2\).