If point B (2, -3) was translated by the rule (x,y)→(x−6,y)

Question

what would the coordinate of  B′
 be

Answer 1

To apply the translation rule \((x,y) \rightarrow (x-6,y)\) to point \(B(2, -3)\), we will subtract 6 from the x-coordinate while keeping the y-coordinate the same.

1. Start with the original coordinates of point \(B\):

   • \(x = 2\)
   • \(y = -3\)

2. Apply the translation:

   • New x-coordinate: \(2 - 6 = -4\)
   • New y-coordinate: \(-3\) (unchanged)

Thus, the coordinates of point \(B'\) after the translation are \((-4, -3)\).

Answer 2

If B′
 is reflected over the x axis, what would the coordinate of B"
 be?

Answer 3

To reflect a point over the x-axis, you keep the x-coordinate the same and change the sign of the y-coordinate.

From the previous result, the coordinates of point \(B'\) are \((-4, -3)\).

To reflect \(B'\) over the x-axis:

1. Keep the x-coordinate: \(-4\)
2. Change the sign of the y-coordinate: \(-(-3) = 3\)

Thus, the coordinates of point \(B''\) after the reflection over the x-axis are \((-4, 3)\).