Question

Where is point B after a translation of 5 unit right, then 4 units up, followed by a rotation of 180° around the origin. (Click Here for Help Video)(1 point) Point B's final position is: Skip to navigation page 12 of 13

Answer 1

To determine the final position of point B after the described transformations, we need to follow the steps one by one.

**Step 1: Translation of 5 units to the right**
Let's denote the original coordinates of point B as \((x, y)\). When we translate point B 5 units to the right, the x-coordinate increases by 5.
New coordinates after translation:
\((x + 5, y)\)

**Step 2: Translation of 4 units up**
Now, we translate the new point 4 units up, which increases the y-coordinate by 4.
New coordinates after this translation:
\((x + 5, y + 4)\)

**Step 3: Rotation of 180° around the origin**
To rotate a point \((x, y)\) by 180° around the origin, both coordinates are negated:
New coordinates after rotation:
\((- (x + 5), - (y + 4))\)
This simplifies to:
\((-x - 5, -y - 4)\)

Thus, the final position of point B after the entire transformation sequence is:
\((-x - 5, -y - 4)\)

If you have specific coordinates for point B, you can substitute those values to find the exact final position.