Distance Between Two Points
Algebra, Coordinate Geometry
Intro: Enter two coordinate points; we’ll compute and simplify the distance.
Worked example
- Find distance between $(−3,4)$ and $(5,−2)$.
- Identify coordinates: $A(x_1,y_1)=(-3,4)$ and $B(x_2,y_2)=(5,-2)$.
- Compute differences: $$\begin{aligned} \Delta x &= x_2 - x_1 = 5 - (-3) = 8 \\ \Delta y &= y_2 - y_1 = -2 - 4 = -6 \end{aligned}$$
- Apply distance formula: $$d=\sqrt{(\Delta x)^2+(\Delta y)^2}=\sqrt{8^2+(-6)^2}.$$
- Square and add: $$8^2=64,\quad (-6)^2=36,\quad 64+36=100.$$
- Take the square root: $$d=\sqrt{100}=10.$$
- Conclusion: $$\boxed{d=10}.$$
- Optional check (Pythagorean view): The horizontal/vertical legs are $|\Delta x|=8$ and $|\Delta y|=6$, so the right triangle has hypotenuse $\sqrt{8^2+6^2}=\sqrt{64+36}=\sqrt{100}=10$ ✔️.
FAQs
Can I enter decimals?
Yes—decimals, fractions, and integers are supported.
Do negatives matter?
No—differences are squared, so the final distance is always non-negative.
Why choose Mathix?
- Get clear, step-by-step solutions that explain the “why,” not just the answer.
- See the rules used at each step (power, product, quotient, chain, and more).
- Optional animated walk-throughs to make tricky ideas click faster.
- Clean LaTeX rendering for notes, homework, and study guides.
Distance formula
- Δx = x2 − x1, Δy = y2 − y1
- (Δx)^2 + (Δy)^2
- d = √((Δx)^2 + (Δy)^2)