QUESTION IMAGE
Question
which is another way to name \\(\overrightarrow{pm}\\)?
\\(\bullet\\) \\(w\\) \\(\bullet\\) \\(n\\) \\(\bullet\\) \\(a\\) \\(\bullet\\) \\(p\\) \\(\bullet\\) \\(t\\) \\(\bullet\\) \\(y\\) \\(\bullet\\) \\(m\\)
\\(\bigcirc\\) ray pt
\\(\bigcirc\\) ray pa
\\(\bigcirc\\) ray mp
\\(\bigcirc\\) raywm
\\(\bigcirc\\) ray ny
Brief Explanations
A ray is named by its endpoint first, then another point on the ray. $\overrightarrow{PM}$ has endpoint \( P \) and goes through \( M \). We check each option:
- Ray PT: PT is on the same line as PM (since P, T, Y, M are colinear in the direction of the ray from P), so Ray PT starts at P and goes through T (and thus through M as well, since T is between P and M). Wait, no—wait, the ray $\overrightarrow{PM}$ starts at P and goes through M. Let's re - examine the number line: W, N, A, P, T, Y, M are in order, with the ray going to the right (from W to M direction is left - to - right? Wait, the arrow on the line is to the right (from W - N - A - P - T - Y - M with the arrow at the end near M). So $\overrightarrow{PM}$ starts at P and goes through T, Y, M. Now, let's check each ray:
- Ray PT: Starts at P, goes through T (and then Y, M). So it's the same ray as $\overrightarrow{PM}$ because it has the same endpoint (P) and is in the same direction (passes through points on the same line beyond P towards M). Wait, no, maybe I made a mistake. Wait, the options: Ray WM: starts at W, goes through M. But $\overrightarrow{PM}$ starts at P. Ray NY: starts at N, goes through Y. Ray PA: starts at P, goes through A (which is in the opposite direction of M, since A is to the left of P). Ray MP: starts at M, goes through P (opposite direction of $\overrightarrow{PM}$). Ray PT: starts at P, goes through T (which is on the way to M, since P - T - Y - M). So Ray PT is the same ray as $\overrightarrow{PM}$ because they have the same endpoint (P) and lie on the same line with the same direction (since T is between P and M, the ray from P through T will pass through M as well). Wait, but let's check the order again. The points are W, N, A, P, T, Y, M with the arrow pointing to the right (towards M). So the ray $\overrightarrow{PM}$ starts at P and goes through T, Y, M. Ray PT starts at P and goes through T (and then Y, M). So they are the same ray. Wait, but maybe the correct answer is Ray WM? No, Ray WM starts at W. Wait, no, I think I messed up. Wait, the problem is to find another name for $\overrightarrow{PM}$. Let's recall the definition of a ray: a ray is named by its endpoint and any other point on the ray. So $\overrightarrow{PM}$ has endpoint P and passes through M. So we need a ray with endpoint P and passing through a point that is on the same ray (i.e., in the direction from P towards M). Let's list the points in order: W --- N --- A --- P --- T --- Y --- M (left to right, with the arrow on the right end). So from P, moving right (the direction of the ray) we have P, T, Y, M. So the ray from P through T (Ray PT) will include M, because T is between P and M. So Ray PT is the same as $\overrightarrow{PM}$ because they share the same endpoint (P) and are colinear in the same direction. Wait, but let's check the other options again:
- Ray PA: goes from P to A, which is left (opposite direction of M).
- Ray MP: goes from M to P (opposite direction of $\overrightarrow{PM}$).
- Ray WM: goes from W to M, which starts at W, not P.
- Ray NY: goes from N to Y, starts at N.
- Ray PT: starts at P, goes to T (and then Y, M), so it's the same ray as $\overrightarrow{PM}$. Wait, but maybe the answer is Ray WM? No, because $\overrightarrow{PM}$ starts at P. Wait, I think I made a mistake. Wait, the ray $\overrightarrow{PM}$: endpoint P, direction towards M. So any ray with endpoint P and passing through a point on the line beyond P towards M is the same ray. So P, T, Y, M are in order, so from P, through T (which is on the way to M) is…
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Ray PT