Coordinate Representation Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
Plot points A(2,5)A(2, 5), B(−3,1)B(-3, 1), C(0,−4)C(0, -4) on the coordinate plane and find the distance from AA to BB.

Solution

  1. 1
    Step 1: Plot each point: AA is 22 right, 55 up; BB is 33 left, 11 up; CC is on the yy-axis, 44 down.
  2. 2
    Step 2: Distance AB=(xB−xA)2+(yB−yA)2=(−3−2)2+(1−5)2AB = \sqrt{(x_B - x_A)^2 + (y_B - y_A)^2} = \sqrt{(-3-2)^2 + (1-5)^2}.
  3. 3
    Step 3: =(−5)2+(−4)2=25+16=41≈6.40= \sqrt{(-5)^2 + (-4)^2} = \sqrt{25 + 16} = \sqrt{41} \approx 6.40.

Answer

AB=41≈6.40AB = \sqrt{41} \approx 6.40 units.
The coordinate plane assigns a unique ordered pair (x,y)(x, y) to every point. The distance formula is an application of the Pythagorean theorem: the horizontal and vertical differences form the legs of a right triangle.

About Coordinate Representation

Describing geometric objects precisely using ordered pairs (x,y)(x, y) or triples (x,y,z)(x, y, z) in a coordinate system.

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More Coordinate Representation Examples

Example 2 medium

Write the equation of the circle with centre [formula] and radius [formula] in standard form. Verify

Example 3 easy

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

Example 4 hard

Three vertices of a parallelogram are [formula], [formula], [formula]. Using coordinate methods, fin

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