Distance between two points
Find how far apart two points are on a graph, using the distance formula.
The distance formula is the Pythagorean theorem in disguise. For points (x1, y1) and (x2, y2): d = √((x2 − x1)² + (y2 − y1)²).
Example: from (−2, 1) to (4, 9). The x change is 6 and the y change is 8, so d = √(36 + 64) = 10.
Classic Graphing 84
Start on the main screen: Press 2nd then mode (QUIT) to get back to the home screen. Pressing clear on a menu also backs out of it.
Open the root with 2nd and x², then an opening bracket. Type (4 − (−2)) squared. Use the (−) key for the negative number.
2nd√x²(4−(−)2)x²Add (9 − 1) squared, close the root bracket and press enter.
+(9−1)x²)enter
You should see(9−1)² 10
Natural Scientific 991
Start on the main screen: Press MENU, then 1 (Calculate) to return to the main calculation screen. AC clears the line you are on.
Press the root key and type (4 − (−2)) squared. Use the (−) key for the negative number.
√(4−(−)2)x²Add (9 − 1) squared, press = and read the distance.
+(9−1)x²=
You should see(9−1)² 10
RPN Scientific 15
Start on the main screen: There is no menu to leave. Press the back arrow to clear a number you are typing, or CLx (g then back arrow) to clear the X register.
Work out the x change: key in 4, ENTER, 2, CHS, then subtract. Square it with g then √x.
4ENTER2CHS−gx²√xWork out the y change, 9 − 1, and square it.
9ENTER1−gx²√xAdd the two squares and take the square root.
+√x
You should see10.0000
Tips
- Squaring removes the sign, so it does not matter which point you call first.
- Put brackets around each difference. Without them, the order of operations changes the answer.
Related guides
- Use the Pythagorean theoremFind the long side (hypotenuse) of a right triangle from the two shorter sides.
- Find the midpoint of a segmentAverage the x values and the y values of two points to find the point halfway between them.
- Find the slope of a lineWork out rise over run between two points, such as (2, 1) and (6, 4).