Applications of Distance Formula
Applications of the distance formula use side lengths found from coordinates to identify geometric properties such as equal sides, right triangles, rectangles, or squares.
Practice This ConceptMain explanation
Teacher explanation
When vertices of a figure are given as coordinates, the distance formula helps find side lengths and sometimes diagonals. After finding lengths, we compare them with known properties: equal sides for isosceles triangle, three equal sides for equilateral triangle, Pythagoras check for right triangle, and equal diagonals with opposite sides equal for rectangles.
Example
If AB = 5, BC = 5, and AC = 8, then triangle ABC is isosceles because two sides are equal.
Simple analogy
Calculate first, classify later.
Common confusion
Students may calculate only one side and decide the figure type without comparing all required sides.
Exam tip
Write all relevant lengths clearly before naming the triangle or quadrilateral. Marks are often given for comparison, not only calculation.
Study the applications of distance formula diagram carefully
Use the labelled diagram to keep applications of distance formula clear in short answers and revision.
What this diagram makes clear
This diagram keeps the labels and direction of applications of distance formula in the right order.
Where this helps in exams
Use this for labelled diagram work and short exam answers on applications of distance formula.
Revision cue
Revise applications of distance formula through the labels before writing the answer.
Answer writing and exam use
1-mark use
Write the exact meaning of applications of distance formula in one clean line.
2-mark use
Define applications of distance formula and add one example or condition.
3-mark use
Explain applications of distance formula, show the method or example, and mention the common mistake.
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