Question

Point P'(1,5)P ′ (1,5) is the image of P(-3,1)P(−3,1) under a translation.

Answer 1

Answer:

The translation vector is (4, 4).

Vectorially speaking, a translation between two distinct point on cartesian plane is described by the following formula:

P'(x,y) = P(x,y) + T(x,y)P

′

(x,y)=P(x,y)+T(x,y) (1)

Where:

P(x,y)P(x,y) - Original point.

P'(x,y)P

′

(x,y) - Translated point.

T(x,y)T(x,y) - Translation vector.

If we know that P(x,y) = (-3, 1)P(x,y)=(−3,1) and P'(x,y) = (1,5)P

′

(x,y)=(1,5) , then the translation vector is:

T(x,y) = P'(x,y) - P(x,y)T(x,y)=P

′

(x,y)−P(x,y)

T(x,y) = (1,5) - (-3, 1)T(x,y)=(1,5)−(−3,1)

T(x,y) = (4,4)T(x,y)=(4,4)

The translation vector is (4, 4).