What are the coordinates of point B′ if the translation vector (7,−5) is applied to triangle ABC to produce the image triangle A′B′C′?
Without knowing the coordinates of point B in triangle ABC, we cannot determine the exact coordinates of point B′ in triangle A′B′C′. However, we can use the vector addition rule to find the translation of any point in the plane by adding the translation vector (7, -5) to the vector connecting that point to the origin.
For example, if point B has coordinates (2, 3) in triangle ABC, the vector connecting it to the origin is OB = <2, 3>. To find the coordinates of point B′ in triangle A′B′C′, we add the translation vector (7, -5) to OB:
OB′ = OB + (7, -5)
= <2, 3> + <7, -5>
= <9, -2>
Therefore, if point B has coordinates (2, 3) in triangle ABC, then point B′ has coordinates (9, -2) in triangle A′B′C′ after the translation vector (7, -5) is applied.
What if point B was (-8,7)
If point B has coordinates (-8, 7) in triangle ABC, then the vector connecting it to the origin is OB = <-8, 7>. To find the coordinates of point B' in triangle A'B'C' after the translation vector (7, -5) is applied, we add (7, -5) to OB:
OB' = OB + (7, -5)
= <-8, 7> + <7, -5>
= <-1, 2>
Therefore, if point B has coordinates (-8, 7) in triangle ABC, then point B' has coordinates (-1, 2) in triangle A'B'C' after the translation vector (7, -5) is applied.
To find the coordinates of point B′, we need to apply the translation vector (7,-5) to the coordinates of point B.
Let's assume the coordinates of point B are (x, y).
To apply the translation vector, we add the x-component (7) to the x-coordinate of point B and the y-component (-5) to the y-coordinate of point B.
Thus, the coordinates of point B′ would be (x + 7, y - 5).