Question

A pentagon was graphed on a coordinate grid and then was translated 10 units left and 6 units up. If one of the vertices of the original pentagon was located at (9,0), what is the ordered pair of this vertex of the new pentagon after the transformation?

a) (-1, 6)
b) (-1, -6)
c) (19, 6)
d) (19, -6)

Answer 1

The original vertex (9, 0) undergoes a translation of 10 units left and 6 units up, resulting in the new coordinates (-1, 6).Thus, the correct option is a) (-1, 6).

Step-by-step explanation:

In the given problem, the coordinates of the original vertex are (9, 0), and a translation of 10 units left and 6 units up is applied to the pentagon on the coordinate grid. Translation involves shifting each coordinate of a point by a specific amount in both the x and y directions.

For the x-coordinate, subtracting 10 from the original value represents the 10-unit leftward shift. Consequently, the new x-coordinate is calculated as
`\(9 - 10 = -1\)` . Similarly, for the y-coordinate, adding 6 to the original value accounts for the 6-unit upward shift, resulting in the new y-coordinate
`\(0 + 6 = 6\).` Therefore, the transformed coordinates for the original vertex are (-1, 6).

This means that the point, originally at (9, 0), has shifted to the left by 10 units and upward by 6 units. The final ordered pair corresponds to option (a), confirming that the correct position of the vertex after the translation is (-1, 6). Understanding the principles of coordinate geometry and translation is essential for accurately determining the new positions of points on a grid following geometric transformations.

Therefore, the correct option is a) (-1, 6).