Distance Formula — Flashcards
ICSE · Class 9 · Mathematics
24 flashcards for Distance Formula (ICSE Class 9 Mathematics) to test yourself on key terms and facts. Part of the ICSE Class 9 Mathematics syllabus.
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Formula for the distance between two points A(x1, y1) and B(x2, y2)
Answer
Distance Formula: AB = √((x2 - x1)² + (y2 - y1)²) = √((x1 - x2)² + (y1 - y2)²) What each symbol means: - A(x1, y1) and B(x2, y2) are the two given points - x-coordinates are called abscissae - y-coor…
Solve: Find the distance between the points (3,6) and (0,2).
Answer
Step 1: Use AB = √((x2 - x1)² + (y2 - y1)²) Step 2: Take (x1, y1) = (3,6) and (x2, y2) = (0,2) Step 3: AB = √((0-3)² + (2-6)²) Step 4: AB = √(9 + 16) Step 5: AB = √25 = 5 Answer: 5 units…
Solve: Find the distance between the origin and the point (-12,5).
Answer
Step 1: Use distance from origin: √(x² + y²) Step 2: Substitute x = -12, y = 5 Step 3: Distance = √((-12)² + 5²) Step 4: Distance = √(144 + 25) Step 5: Distance = √169 = 13 Answer: 13 units…
Solve: Find the distance between the origin and the point (15,-8).
Answer
Step 1: Use distance from origin: √(x² + y²) Step 2: Substitute x = 15, y = -8 Step 3: Distance = √(15² + (-8)²) Step 4: Distance = √(225 + 64) Step 5: Distance = √289 = 17 Answer: 17 units…
Why does the distance formula use squares of coordinate differences?
Answer
The differences in x and y form the two perpendicular sides of a right-angled triangle. Pythagoras' Theorem gives: AB² = AC² + BC² So the distance becomes: AB = √((x2 - x1)² + (y2 - y1)²) Squaring …
Solve: KM is 13 units long. K = (2,5) and M = (x,-7). Find x.
Answer
Step 1: Use KM = √((x - 2)² + (-7 - 5)²) Step 2: Set KM = 13 Step 3: 13 = √((x - 2)² + (-12)²) Step 4: 169 = (x - 2)² + 144 Step 5: (x - 2)² = 25 Step 6: x - 2 = 5 or x - 2 = -5 Step 7: x = 7 or x = -…
When do you use the distance from origin formula? Solve one example.
Answer
Use √(x² + y²) when one point is the origin (0,0). Example: Distance from origin to (-12,5) = √((-12)² + 5²) = √(144 + 25) = √169 = 13 units Answer: Use it whenever one endpoint is (0,0).
Find the coordinates of points on the x-axis that are 5 units away from (6,-3).
Answer
Step 1: A point on the x-axis is written as (x,0) Step 2: Use distance formula: 5 = √((x - 6)² + (0 - (-3))²) Step 3: 5 = √((x - 6)² + 3²) Step 4: 25 = (x - 6)² + 9 Step 5: (x - 6)² = 16 Step 6: x - 6…
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