15. What is the image of the point \( A(-2,8) \) after a translation along vector \( (5,-10) \) \( (-7,-2) \) \( (3,18) \) \( (3,-2) \) \( (-12,18) \)

To find the image of the point \( A(-2, 8) \) after a translation along the vector \( (5, -10) \), you can use the following formula for translation: \[ \text{New point} = (x + a, y + b) \] where \( (a, b) \) is the translation vector. Given: - Original point \( A(-2, 8) \) - Translation vector \( (5, -10) \) Applying the formula: \[ x' = -2 + 5 = 3 \] \[ y' = 8 + (-10) = -2 \] So, the image of the point \( A \) after the translation is \( (3, -2) \). **Answer:** \( \boxed{(3,\ -2)} \)