Question

Is YZ a diameter? Explain your reasoning.

a) Yes, it is a diameter because it connects two points on the circumference.
b) No, it is not a diameter because it does not pass through the center.
c) Cannot determine from the given information.
d) Yes, it is a diameter because the image provided confirms it.

Answer 1

Without confirming that line segment YZ passes through the center of the circle, we cannot conclude that it is a diameter; the best answer is option c): Cannot determine from the given information.

b) No, it is not a diameter because it does not pass through the center.

Step-by-step explanation:

The question, 'Is YZ a diameter?' cannot be answered definitively without additional information. The quality of being a diameter is not solely dependent on a line segment connection two points on the circumference of a circle. Instead, the defining characteristic of a diameter is that it must pass through the center of the circle.

Hence, without information confirming that line segment YZ passes through the center of the circle, we cannot conclude that it is a diameter. If YZ does not pass through the center, then it would be considered a chord, not a diameter. Therefore, the best answer based only on the information provided is option c): Cannot determine from the given information.

b) No, it is not a diameter because it does not pass through the center.