Question
A point is plotted on a polar coordinate grid. The point is on the positive vertical axis on the fourth circle from the pole.
Question
Use the image to answer the question.
Which polar coordinates represent the point plotted on the graph? Select all that apply.
(1 point)
Responses
left-parenthesis negative 4 comma 90 degree-sign right-parenthesis
Image with alt text: left-parenthesis negative 4 comma 90 degree-sign right-parenthesis
left-parenthesis 4 comma 90 degree-sign right-parenthesis
Image with alt text: left-parenthesis 4 comma 90 degree-sign right-parenthesis
left-parenthesis 4 comma negative 90 degree-sign right-parenthesis
Image with alt text: left-parenthesis 4 comma negative 90 degree-sign right-parenthesis
left-parenthesis negative 4 comma 270 degree-sign right-parenthesis
Image with alt text: left-parenthesis negative 4 comma 270 degree-sign right-parenthesis
left-parenthesis negative 4 comma negative 270 degree-sign right-parenthesis
Image with alt text: left-parenthesis negative 4 comma negative 270 degree-sign right-parenthesis
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Question
Use the image to answer the question.
Which polar coordinates represent the point plotted on the graph? Select all that apply.
(1 point)
Responses
left-parenthesis negative 4 comma 90 degree-sign right-parenthesis
Image with alt text: left-parenthesis negative 4 comma 90 degree-sign right-parenthesis
left-parenthesis 4 comma 90 degree-sign right-parenthesis
Image with alt text: left-parenthesis 4 comma 90 degree-sign right-parenthesis
left-parenthesis 4 comma negative 90 degree-sign right-parenthesis
Image with alt text: left-parenthesis 4 comma negative 90 degree-sign right-parenthesis
left-parenthesis negative 4 comma 270 degree-sign right-parenthesis
Image with alt text: left-parenthesis negative 4 comma 270 degree-sign right-parenthesis
left-parenthesis negative 4 comma negative 270 degree-sign right-parenthesis
Image with alt text: left-parenthesis negative 4 comma negative 270 degree-sign right-parenthesis
Skip to navigation
Answers
GPT-4o mini
In polar coordinates, the first value represents the radius (distance from the pole) and the second value represents the angle measured from the positive x-axis (counter-clockwise).
The point described is located on the positive vertical axis at a radius of 4 units from the pole, which would be at an angle of 90 degrees. Therefore, the correct polar coordinates for the point on the positive vertical axis at that distance would be:
- \((4, 90^\circ)\)
Now, let's analyze the responses:
1. \((-4, 90^\circ)\) - This is not correct; a negative radius means the point would be located in the opposite direction.
2. \((4, 90^\circ)\) - This is correct.
3. \((4, -90^\circ)\) - While this represents a point that is also on the vertical axis (downward) but at a distance of 4 units, it refers to the same location but in a clockwise direction. It is still valid.
4. \((-4, 270^\circ)\) - This point, being negative in radius, is not correct.
5. \((-4, -270^\circ)\) - This point is also incorrect for the same reason as above.
Thus, the polar coordinates that represent the point plotted on the graph are:
- \((4, 90^\circ)\)
- \((4, -90^\circ)\)
The point described is located on the positive vertical axis at a radius of 4 units from the pole, which would be at an angle of 90 degrees. Therefore, the correct polar coordinates for the point on the positive vertical axis at that distance would be:
- \((4, 90^\circ)\)
Now, let's analyze the responses:
1. \((-4, 90^\circ)\) - This is not correct; a negative radius means the point would be located in the opposite direction.
2. \((4, 90^\circ)\) - This is correct.
3. \((4, -90^\circ)\) - While this represents a point that is also on the vertical axis (downward) but at a distance of 4 units, it refers to the same location but in a clockwise direction. It is still valid.
4. \((-4, 270^\circ)\) - This point, being negative in radius, is not correct.
5. \((-4, -270^\circ)\) - This point is also incorrect for the same reason as above.
Thus, the polar coordinates that represent the point plotted on the graph are:
- \((4, 90^\circ)\)
- \((4, -90^\circ)\)