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Coordinate geometryGeometryMiddle schoolabout 0:43

Find the distance between (3, -4) and (-3, 4): animated lesson

A narrated, step-by-step coordinate geometry video lesson with captions. Final answer: d = 10.

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Video with a synthetic English voice and captions. Pick another language for subtitles in that language, or open the interactive version.

Video narrated by a synthetic voice (Piper TTS, en_US-ljspeech-high voice (LJ Speech dataset, public domain)); the steps come from our maths engine and the answer was checked independently. Download MP4 (0.3 MB) · Captions (WebVTT)

Steps on screen

1. The problem
Worked example
Find the distance between (3, -4) and (-3, 4).
2. Steps, part 1
1. $(x_1, y_1) = (3, -4),\quad (x_2, y_2) = (-3, 4)$
  Label the points
2. $\Delta x = -6,\quad \Delta y = 8$
  Find the horizontal and vertical differences
3. $(-6)^2 + (8)^2 = 36 + 64 = 100$
  Square the differences and add them
4. $d = \sqrt{100} = 10$
  Take the square root
3. Steps, part 2
1. $M = \left(\frac{3 + (-3)}{2}, \frac{-4 + 4}{2}\right) = (0, 0)$
  Midpoint (average of the coordinates)
4. The answer
$d = 10$
d = √(-6² + 8²) = 10
5. Check
- d² = 100 matches Δx² + Δy² = 100

Transcript

The problem. Here is the problem: Find the distance between (3, negative 4) and (negative 3, 4). Find the straight-line (Euclidean) distance between two points in the plane.

Steps, part 1. Label the points. Find the horizontal and vertical differences. Square the differences and add them. Take the square root.

Steps, part 2. Midpoint (average of the coordinates).

The answer. So the answer is d equals 10. The distance formula is the Pythagorean theorem applied to the right triangle whose legs are the horizontal and vertical differences between the points.

Check. d squared equals 100 matches deltax squared plus deltay squared equals 100.

About coordinate geometry

Distance, midpoint and slope between points in the coordinate plane.

Find the distance between (3, -4) and (-3, 4) (Lesson)