Coordinate Plane Math Example 2

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Example 2

medium
Find the distance between points (1,2)(1, 2) and (4,6)(4, 6).

Solution

  1. 1
    Use the distance formula: d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}.
  2. 2
    Substitute: d=(4−1)2+(6−2)2=9+16d = \sqrt{(4-1)^2 + (6-2)^2} = \sqrt{9 + 16}.
  3. 3
    Simplify: d=25=5d = \sqrt{25} = 5.

Answer

d=5d = 5
The distance formula is derived from the Pythagorean theorem. The horizontal and vertical differences form the legs of a right triangle, and the distance is the hypotenuse.

About Coordinate Plane

A two-dimensional surface formed by two perpendicular number lines — the horizontal xx-axis and the vertical yy-axis — intersecting at the origin (0,0)(0, 0). Every point on the plane is uniquely identified by an ordered pair (x,y)(x, y) giving its horizontal and vertical distances from the origin.

Learn more about Coordinate Plane →

More Coordinate Plane Examples

Example 1 easy

In which quadrant is the point [formula] located?

Example 3 easy

Plot the point [formula]. Is it above or below the [formula]-axis?

Example 4 medium

Find the midpoint of the segment connecting [formula] and [formula].

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