TACHS: Classification: a dot on the crossing
Learn the two conditions these figures share, a true crossing and a dot exactly on it, and test both in every choice while ignoring length and angle.
What do the example figures share when their lines all have different lengths and angles?
Short answer
Two segments cross, each one continuing past the meeting point, and the dot sits exactly on that crossing. Check both conditions in every choice. Length, angle and position in the frame do not matter.
Know first: What a line segment and its endpoints are
Step 1 of 5
Two conditions, checked together
In these questions each example shows two straight line segments and one dot. The segments can be long or short, steep or flat, and the crossing can be lopsided. None of that matters.
What matters is two conditions together. Wrong choices usually break exactly one of them, so a choice that passes one check can still be wrong.
| Condition | Passes | Fails |
|---|---|---|
| 1. The segments cross | Each segment continues past the meeting point on both sides, like an X or a plus sign | A V or an L, where they touch only at their ends. Two segments that never touch |
| 2. The dot is on the crossing | The dot is centered exactly on the meeting point | A dot near the crossing, at the end of a segment, or in a gap |
A figure belongs only if it passes both.
Step 2 of 5
Test both conditions in every choice
Worked example: Ignore the look, test the conditions
Example 1: an X made of two equal segments, with a dot at the center.
Example 2: a plus sign shifted toward the left of its frame, its flat segment longer than its upright one, with a dot where they cross.
Example 3: a steep segment crossing a nearly flat one about a third of the way along it, with a dot at that crossing.
Which choice belongs with them?
- AA V shape, with a dot at its point
- BAn X, with the dot slightly above the center
- CAn X, with the dot at the top end of one segment
- DTwo segments that do not touch, with a dot in the gap
- EA long flat segment crossed near its right end by a short steep one, with the dot exactly on the crossing
- 1
Name the property
Two segments cross in their middles, and a dot marks the crossing.
- 2
Check condition 1
The V shape meets only at the bottom ends of its segments, so it fails. The two separate segments never touch, so they fail too.
- 3
Check condition 2
The X with the dot slightly above the center fails. So does the X with the dot at the top end of a segment.
- 4
Confirm the answer
The long flat segment crossed by a short steep one near its right end looks unlike the examples, but each segment continues past the crossing, and the dot is exactly on it.
- 5
See why the other choices are there
The X with the dot above center looks the most like Example 1. The choice that looks most familiar at a glance is often the trap.
Answer
A long flat segment crossed near its right end by a short steep one, with the dot exactly on the crossing.
Wrong: A dot a little above the crossing is close enough.
Right: A dot exactly on the crossing is the only placement that fits.
Condition 2 is about exact position. A dot beside the crossing fails it, so look at the very center of the meeting point.
Step 3 of 5
Check the conditions on your own
Check yourself · Question 1
A figure shows two segments forming an L: they meet at their ends, at a right angle, with a dot at the corner. Which statement is true?
Answer: B
The dot is on the meeting point, so condition 2 is fine. But neither segment continues past that point, so they touch without crossing.
Check yourself · Question 2
Example 1: a tilted X with a dot at the crossing. Example 2: a long upright segment crossed near its top by a short flat one, with a dot on the crossing. Example 3: two nearly flat segments crossing at a narrow angle, with a dot on the crossing. Which choice belongs with them?
Answer: D
Both segments continue past the meeting point, and the dot is exactly on it. Where the crossing falls along the segments does not matter.
Trap answer: Two crossing segments, with the dot just to the right of the crossing
Dot near the crossing
- Why it looks right
- It passes condition 1 and the dot is almost right, so it feels like a match.
- Why it's wrong
- Every example puts the dot exactly on the crossing. A dot beside it breaks condition 2.
- The right answer
- The segments crossing near their left ends, with the dot exactly on the crossing.
Common mistake
I picked the choice that looked most like one of the examples.
- Why it's tempting
- A figure that resembles an example feels safe, especially when time is short.
- Do this instead
- Wrong choices are often built to look familiar. Test condition 1, then condition 2, and let the tests decide.
Step 4 of 5
What to remember
Remember
- The segments must cross, each continuing past the meeting point. A V, an L or a gap fails.
- The dot must sit exactly on the crossing, not near it and not at an end.
- Length, angle and position in the frame change freely, so ignore them.
Step 5 of 5
Practice on a real question
Use what you just learned on this question, then check the explanation.
Try another one
In your own words
In the practice question, which condition did each wrong choice break, and which one looked most like an example?