Question

match each drawing on the left with its correct geometric notation on the right. some of the answer choices on the right will not be used.
click and hold an item in one column, then drag it to the matching item in the other column. be sure your cursor is over the target before releasing. the target will highlight or the cursor will change. need help? watch this video.
incorrect. the correct notation contains a tiny version of
submit

Explanation:

Step1: Analyze the first drawing (segment with endpoints A, B)

A segment with two endpoints (no arrows) is a line segment, denoted by \( \overline{AB} \) (or \( AB \) as a length, but here the notation with the bar is for the segment). Wait, the first left drawing: two endpoints, so it's a line segment. The right options: \( AB \) (length) or \( \overline{AB} \). Wait, the first left figure: points A and B with a segment (no arrows), so notation is \( \overline{AB} \) (line segment) or \( AB \) (length). But let's check each:

1. First left drawing: two endpoints (A, B), no arrows. So it's a line segment. The notation for a line segment is \( \overline{AB} \) (or \( AB \) as the length, but in geometric notation, the segment is \( \overline{AB} \)). Wait, the right options include \( AB \) (maybe as the segment? Wait, no: \( \overline{AB} \) is segment, \( \overrightarrow{AB} \) is ray, \( \overleftrightarrow{AB} \) is line, \( \overrightarrow{BA} \) is ray opposite, \( AB \) is length. Wait, let's re-express:

- First left: segment AB (endpoints A, B, no arrows) → notation \( \overline{AB} \) (or \( AB \) if considering length, but in the options, \( AB \) is there. Wait, maybe the first left is a segment, so \( AB \) (length) or \( \overline{AB} \). Wait, the options: \( \overrightarrow{AB} \) (ray from A to B), \( \overline{AB} \) (segment), \( \overleftrightarrow{AB} \) (line), \( \overrightarrow{BA} \) (ray from B to A), \( AB \) (length).

Wait, let's list each left drawing:

1. First left: A---B (two endpoints, no arrows) → line segment AB → notation \( \overline{AB} \) or \( AB \). But in the options, \( \overline{AB} \) is present, and \( AB \) is present. Wait, maybe the first is \( AB \) (length) or \( \overline{AB} \). Wait, the second left: A---B with an arrow on the left (so it's a ray? No, left arrow: the segment has a left arrow, meaning it's a ray? Wait, no:

Wait, standard geometric notations:

- Line segment: two endpoints, no arrows: \( \overline{AB} \)
- Ray: one endpoint, one arrow: \( \overrightarrow{AB} \) (starts at A, goes through B)
- Line: two arrows: \( \overleftrightarrow{AB} \)
- Ray opposite: \( \overrightarrow{BA} \) (starts at B, goes through A)
- Line segment: \( \overline{AB} \)
- Ray: \( \overrightarrow{AB} \) (A is endpoint, arrow at B)
- Line: \( \overleftrightarrow{AB} \) (arrows at both ends)
- Ray: \( \overrightarrow{BA} \) (B is endpoint, arrow at A)

Wait, let's re-express each left drawing:

1. First left: A---B (no arrows) → line segment AB → notation \( \overline{AB} \) (or \( AB \) as length, but in the options, \( AB \) is there. Wait, the options include \( AB \) (maybe as the segment). Wait, the first left is a segment, so \( AB \) (length) or \( \overline{AB} \).

2. Second left: A---B with an arrow on the left (so the line has a left arrow, meaning it's a ray? No, the left arrow: the segment is A---B with a left arrow, so it's a ray starting at B? No, wait, the arrow direction: if the left end has an arrow, that means the line extends infinitely to the left, so the segment is part of a line with a left arrow, so it's a ray? No, maybe it's a line with a left arrow, so the notation is \( \overleftrightarrow{AB} \)? No, \( \overleftrightarrow{AB} \) has arrows at both ends. Wait, the second left: A---B with a left arrow (so only left arrow), so it's a ray? No, a ray has one arrow. Wait, maybe the second left is a line with a left arrow, meaning it's a ray starting at B? No, I'm confused. Wait, let's check the options:

Options on the right:

- \( \overrightarrow{AB} \): ray from A to B (A is endpoint, arrow at B)
- \( \overline{AB} \): segment AB (no arrows)
- \( \overleftrightarrow{AB} \): line AB (arrows at both ends)
- \( \overrightarrow{BA} \): ray from B to A (B is endpoint, arrow at A)
- \( AB \): length of segment AB

Now, left drawings:

1. First left: A---B (two endpoints, no arrows) → segment AB → notation \( \overline{AB} \) (or \( AB \) as length). But in the options, \( \overline{AB} \) is present, and \( AB \) is present. Wait, maybe the first is \( AB \) (length) or \( \overline{AB} \). Wait, the fifth option is \( AB \), which is the length, but the segment is \( \overline{AB} \). So first left: \( \overline{AB} \)?

Wait, no, let's do each:

1. First left: A---B (no arrows) → line segment → \( \overline{AB} \) (option 2: \( \overline{AB} \))

2. Second left: A---B with a left arrow (so the line has a left arrow, meaning it's a ray? No, the left arrow: the segment is A---B with a left arrow, so it's a ray starting at B? No, the arrow is on the left end, so the line extends infinitely to the left, so the segment is part of a ray that starts at B and goes left? No, that would be \( \overrightarrow{BA} \) (ray from B to A). Wait, the second left: A---B with a left arrow (so the left end has an arrow), so the ray is from B to A (since the arrow is on the left, towards A). So \( \overrightarrow{BA} \) (option 4: \( \overrightarrow{BA} \))

3. Third left: A---B with arrows at both ends → line AB → \( \overleftrightarrow{AB} \) (option 3: \( \overleftrightarrow{AB} \))

4. Fourth left: A---B with an arrow at the right (so ray from A to B) → \( \overrightarrow{AB} \) (option 1: \( \overrightarrow{AB} \))

Wait, let's confirm:

- Segment: two endpoints, no arrows → \( \overline{AB} \) (second right option)
- Ray with left arrow (so starts at B, goes to A) → \( \overrightarrow{BA} \) (fourth right option)
- Line with arrows at both ends → \( \overleftrightarrow{AB} \) (third right option)
- Ray with right arrow (starts at A, goes to B) → \( \overrightarrow{AB} \) (first right option)

So matching:

1. First left (A---B, no arrows) → \( \overline{AB} \) (second right)
2. Second left (A---B with left arrow) → \( \overrightarrow{BA} \) (fourth right)
3. Third left (A---B with both arrows) → \( \overleftrightarrow{AB} \) (third right)
4. Fourth left (A---B with right arrow) → \( \overrightarrow{AB} \) (first right)

Wait, but the first left: is it a segment or a length? The fifth option is \( AB \) (length), but the segment is \( \overline{AB} \). So first left: \( \overline{AB} \) (option 2), second left: \( \overrightarrow{BA} \) (option 4), third left: \( \overleftrightarrow{AB} \) (option 3), fourth left: \( \overrightarrow{AB} \) (option 1).

But the problem says "some of the answer choices will not be used", so \( AB \) (fifth option) is not used.

So the matches are:

1. A---B (no arrows) → \( \overline{AB} \)
2. A---B (left arrow) → \( \overrightarrow{BA} \)
3. A---B (both arrows) → \( \overleftrightarrow{AB} \)
4. A---B (right arrow) → \( \overrightarrow{AB} \)

But the user is asking to match, so the correct matches are:

- First left (A---B, no arrows) → \( \overline{AB} \)
- Second left (A---B, left arrow) → \( \overrightarrow{BA} \)
- Third left (A---B, both arrows) → \( \overleftrightarrow{AB} \)
- Fourth left (A---B, right arrow) → \( \overrightarrow{AB} \)

But since the user might need the correct notation for each, let's list:

1. Drawing 1 (A---B, no arrows): \( \overline{AB} \)
2. Drawing 2 (A---B, left arrow): \( \overrightarrow{BA} \)
3. Drawing 3 (A---B, both arrows): \( \overleftrightarrow{AB} \)
4. Drawing 4 (A---B, right arrow): \( \overrightarrow{AB} \)

Answer:

1. First drawing (A---B, no arrows) → \( \overline{AB} \)
2. Second drawing (A---B, left arrow) → \( \overrightarrow{BA} \)
3. Third drawing (A---B, both arrows) → \( \overleftrightarrow{AB} \)
4. Fourth drawing (A---B, right arrow) → \( \overrightarrow{AB} \)

(Note: The fifth option \( AB \) is not used as it represents the length of the segment, not the geometric figure notation.)