Two-point

Two-point

What is it?

From A(x1, y1) and B(x2, y2) first compute m = y2-y1x2-x1 if x2!=x1. Then write y - y1 = m(x - x1), or use point B. If x2=x1 the line is vertical: x=x1. Two-point and midpoint are different jobs: two-point writes the whole line; midpoint names only the halfway pair on the segment.

In simple words

• From A(x1, y1) and B(x2, y2) first compute m = y2-y1x2-x1 if x2!=x1.
• m = y2-y1x2-x1
• x2=x1
• vertical

Important terms

Two-Point: From A(x1, y1) and B(x2, y2) first compute m = y2-y1x2-x1 if x2!=x1. Then write y - y1 = m(x - x1), or use point B. If x2=x1 the line is vertical: x=x1. Two-point and midpoint are different jobs: two-point writes the whole line; midpoint names only the halfway pair on the segment.

What you should learn

• Define and explain two-point.
• Apply two-point to a focused FBISE question.
• Check the answer for correct terms, evidence, working, and units.

Examples

• m = y2-y1x2-x1
• x2=x1
• vertical

CORE UNDERSTANDING

From A(x1, y1) and B(x2, y2) first compute m = y2-y1x2-x1 if x2!=x1. Then write y - y1 = m(x - x1), or use point B. If x2=x1 the line is vertical: x=x1. Two-point and midpoint are different jobs: two-point writes the whole line; midpoint names only the halfway pair on the segment.

EXAM APPLICATION

State the correct term, connect it to the chapter rule or evidence, and use a clear example or calculation.

Full school-level explanation

From A(x1, y1) and B(x2, y2) first compute m = y2-y1x2-x1 if x2!=x1. Then write y - y1 = m(x - x1), or use point B. If x2=x1 the line is vertical: x=x1. Two-point and midpoint are different jobs: two-point writes the whole line; midpoint names only the halfway pair on the segment.

Learn the idea, then use it:

WHAT — TWO-POINT

From A(x1, y1) and B(x2, y2) first compute m = y2-y1x2-x1 if x2!=x1. Then write y - y1 = m(x - x1), or use point B. If x2=x1 the line is vertical: x=x1. Two-point and midpoint are different jobs: two-point writes the whole line; midpoint names only the halfway pair on the segment.

HOW — Use the idea

Identify what is given, select this topic's rule or evidence, apply it one step at a time, and check the result.

CORE UNDERSTANDING

From A(x1, y1) and B(x2, y2) first compute m = y2-y1x2-x1 if x2!=x1. Then write y - y1 = m(x - x1), or use point B. If x2=x1 the line is vertical: x=x1. Two-point and midpoint are different jobs: two-point writes the whole line; midpoint names only the halfway pair on the segment.

Remember

• m = y2-y1x2-x1
• x2=x1
• vertical

Examples

• m = y2-y1x2-x1
• x2=x1
• vertical
• TWO-POINT: From A(x1, y1) and B(x2, y2) first compute m = y2-y1x2-x1 if x2!=x1. Then write y - y1 = m(x - x1), or use point B.

EXAM APPLICATION

State the correct term, connect it to the chapter rule or evidence, and use a clear example or calculation.

Remember

• correct term
• chapter link
• clear application

Examples

• Define first
• Show the rule or evidence
• Check units, labels, and conclusion

Remember

• m = y2-y1x2-x1
• x2=x1
• vertical
• keep the ideas separate
• m = y2-y1x2-x1
• x2=x1
• vertical
• correct term

Deeper understanding

Go beyond memorising Two-point. Connect the definition to reasons, relationships, exceptions, and exam wording.

Common mistakes

Exam focus

Core Idea

Key Points

Simple Check

How to Answer

Exam focus

Quick revision

• m = y2-y1x2-x1
• x2=x1
• vertical
• keep the ideas separate
• Two-Point: From A(x1, y1) and B(x2, y2) first compute m = y2-y1x2-x1 if x2!=x1. Then write y - y1 = m(x -
• WHAT — TWO-POINT: From A(x1, y1) and B(x2, y2) first compute m = y2-y1x2-x1 if x2!=x1. Then write y - y1 = m(x -

Do not merge two-point with a neighbouring idea that uses a different definition, rule, or method.

For long answers on Two-point: define clearly → explain the main parts → give one example → state one exam caution.