In this lesson:
After this lesson, you will:
How would you measure the exact distance?
The distance is the hypotenuse of this right triangle.
For any two points and :
Key insight:
Find the distance between and .
Step 1: Compute differences
Step 2: Square, add, and take the root
Distance between and :
Work it out before advancing...
Order doesn't matter for distance:
But keep a consistent order — it matters for slope.
3D extension (rare on the ACT):
You can now find the distance between any two points.
What comes next:
Triangle with vertices , , .
Perimeter
From our triangle: ,
Isosceles (). Right? → no
Is equidistant from and ?
Distance to :
→ Yes, equidistant.
A triangle has vertices , , .
Compute all three side lengths and classify the triangle.
Is it right? Isosceles? Both?
The distance between and is .
Since -coordinates are equal, this is a horizontal distance:
Which pair is closest: , , ?
AB and BC are tied — both equal .
Problem 1: Find the distance between and .
Problem 2: A triangle has vertices at , , and . Find its perimeter.
Target: 60 seconds each. Go!
Problem 1:
Problem 2:
✓ Distance formula IS the Pythagorean theorem ✓ Squaring eliminates sign issues ✓ Apply three times for perimeter
Square first, then add, then root Don't forget the final square root
Up next: The midpoint formula