Question

Translate the point -(-2,-3) 2 units to the left and 6 units up. What will be the new coordinates of the point -2,3) after translation?

A) (-4, 9)
B) (0, 3)
C) (0, 9)
D) (-4, -3)

Answer 1

The new coordinates of the point (-2, -3) after translating 2 units to the left and 6 units up are D) (-4, -3).

Step-by-step explanation:

In this translation, moving 2 units to the left means subtracting 2 from the x-coordinate, and moving 6 units up means adding 6 to the y-coordinate. The original point (-2, -3) can be expressed as (x₁, y₁), where x₁ = -2 and y₁= -3.

To find the new coordinates after the translation, we apply the translation formulas:

`\[ x_2 = x_1 - \text{leftward shift} = -2 - 2 = -4 \]`

`\[ y_2 = y_1 + \text{upward shift} = -3 + 6 = 3 \]`

Therefore, the new coordinates (x₂, y₂) are (-4, 3). So, the correct answer is D) (-4, -3).

In summary, to obtain the new coordinates, we adjusted the original coordinates by subtracting the leftward shift from the x-coordinate and adding the upward shift to the y-coordinate. The calculations confirm that the final position of the point after the translation is indeed (-4, 3).

Therefore, the correct option is D) (-4, -3).