Answer and Explanation:
To determine which representations do not change the location of the point (6, 110°), we need to consider the polar coordinate system. In this system, a point is represented by its distance from the origin (r) and the angle it makes with the positive x-axis (θ).
In this case, the given point (6, 110°) means that the point is located at a distance of 6 units from the origin and makes an angle of 110 degrees with the positive x-axis.
Let's analyze each representation:
a. (-6, 290°):
- In this representation, the point is located at a distance of -6 units from the origin. However, distances cannot be negative in the polar coordinate system.
- This representation does change the location of the point.
b. (-6, 250°):
- Similar to the previous representation, the point is located at a negative distance from the origin (-6 units), which is not possible.
- This representation also changes the location of the point.
c. (-6, -70°):
- Again, the distance from the origin is negative (-6 units), which is not valid.
- This representation changes the location of the point.
d. (6, -250°):
- In this representation, the point is located at a distance of 6 units from the origin, which is the same as the original point (6, 110°).
- However, the angle is different (-250° instead of 110°), so the representation does change the location of the point.
To summarize, none of the given representations (a, b, c, d) keep the location of the point (6, 110°) unchanged.