Question

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′?

Answer 1

What if point B was (-8,7)

Answer 2

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.

Answer 3

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.