Coordinate Geometry Solver Calculator

Calculator Form

Choose a solver mode, enter the relevant values, and submit to generate answers, equations, and a graph. Results appear above this form.

Solver Mode

x1

y1

x2

y2

m

n

Ax

Ay

Bx

By

Cx

Cy

Point X

Point Y

a

b

c

Center h

Center k

Radius r

Optional Point Qx

Optional Point Qy

Example Data Table

Mode	Sample Inputs	Example Output
Two Point Analysis	A(1, 2), B(7, 10)	Distance = 10, Midpoint = (4, 6)
Section Formula	A(2, 3), B(8, 9), Ratio 1:2	P = (4, 5)
Triangle Solver	A(0, 0), B(4, 0), C(0, 3)	Area = 6, Perimeter = 12
Point and Line	P(3, 2), Line 2x + y - 6 = 0	Distance = 0.894427, Foot = (2.2, 1.6)
Circle Solver	Center (2, -1), Radius 5	Area = 78.539816, Circumference = 31.415927

Formula Used

Distance between two points: d = √[(x2 - x1)² + (y2 - y1)²]

Midpoint: M = ((x1 + x2) / 2, (y1 + y2) / 2)

Slope: m = (y2 - y1) / (x2 - x1)

Two-point line equation: A = y1 - y2, B = x2 - x1, C = x1y2 - x2y1, then Ax + By + C = 0

Internal section formula: P = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n))

Triangle area: Area = |x1(y2-y3) + x2(y3-y1) + x3(y1-y2)| / 2

Triangle centroid: G = ((x1+x2+x3)/3, (y1+y2+y3)/3)

Point to line distance: d = |ax0 + by0 + c| / √(a² + b²)

Foot of perpendicular: F = (x0 - aD, y0 - bD), where D = (ax0 + by0 + c)/(a²+b²)

Circle standard form: (x - h)² + (y - k)² = r²

Circle area and circumference: A = πr², C = 2πr

How to Use This Calculator

Select a solver mode that matches your coordinate geometry task.
Enter only the values needed for that mode.
Click Solve Geometry to process the inputs.
Read the result box above the form for equations and values.
Review the Plotly graph to verify the geometric relationship visually.
Use the CSV or PDF buttons to export the solved output.

FAQs

1. What can this coordinate geometry solver calculate?

It solves distance, midpoint, slope, line equations, internal section points, triangle measurements, point-to-line distance, and circle properties in one page.

2. Does it support graphing after calculation?

Yes. Each solver mode creates a Plotly graph so you can inspect the shape, segment, point, line, or circle visually.

3. Can I use decimals and negative coordinates?

Yes. The form accepts decimal values, integers, and negative coordinates. That makes it useful for classroom work, homework, and technical checking.

4. What happens if the line is vertical?

The calculator marks slope as undefined and still returns the general line equation correctly. Vertical lines are handled without breaking the result.

5. Can this calculator detect invalid triangle inputs?

Yes. If the three points are collinear, the area becomes zero, and the calculator shows an error instead of a misleading triangle result.

6. Does the section formula mode use internal division?

Yes. This version uses internal division with ratio m:n. The result point is placed between the two entered coordinates.

7. Are export options included?

Yes. You can download the result area as CSV for spreadsheet use or as PDF for printing, saving, or sharing.

8. Is this suitable for students and teachers?

Yes. It is useful for learning formulas, checking answers, preparing examples, and understanding coordinate relationships through both numbers and plots.