Section Formula — Flashcards
ICSE · Class 10 · Mathematics
20 flashcards for Section Formula (ICSE Class 10 Mathematics) to test yourself on key terms and facts. Sample: "Solve: A line segment joins A(2, 3) and B"
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See them allSolve: A line segment joins A(2, 3) and B(8, 9). Find the midpoint of AB.
Answer
Step 1: Use the midpoint formula. Midpoint = ((x1 + x2)/2, (y1 + y2)/2) Step 2: Substitute the values. Midpoint = ((2 + 8)/2, (3 + 9)/2) Step 3: Simplify. Midpoint = (10/2, 12/2) = (5, 6) Answer: The…
Find the point P dividing A(1, 4) and B(7, 10) internally in the ratio 1:2.
Answer
Step 1: Use the section formula. P = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)) Step 2: Here m = 1, n = 2, A(1,4), B(7,10). Step 3: Substitute in x-coordinate. x = (1×7 + 2×1)/(1+2) = (7 + 2)/3 = 3 Step 4…
Solve: A point P divides A(3, 2) and B(9, 8) internally in the ratio 2:1. Find P.
Answer
Step 1: Use the section formula. P = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)) Step 2: Here m = 2, n = 1. Step 3: Find x-coordinate. x = (2×9 + 1×3)/(2+1) = (18 + 3)/3 = 7 Step 4: Find y-coordinate. y = …
Find the point that divides A(0, 5) and B(6, 11) internally in the ratio 3:1.
Answer
Step 1: Use the section formula. P = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)) Step 2: Here m = 3, n = 1. Step 3: Calculate x. x = (3×6 + 1×0)/(3+1) = 18/4 = 4.5 Step 4: Calculate y. y = (3×11 + 1×5)/(3+…
Find the point P dividing A(-4, 2) and B(8, -6) internally in the ratio 1:1.
Answer
Step 1: Ratio 1:1 means the point is the midpoint. Step 2: Use midpoint formula. Midpoint = ((x1 + x2)/2, (y1 + y2)/2) Step 3: Substitute values. Midpoint = ((-4 + 8)/2, (2 + -6)/2) Step 4: Simplify.
Solve: A point divides A(5, -1) and B(11, 7) internally in the ratio 2:3. Find its coordinates.
Answer
Step 1: Use the section formula. P = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)) Step 2: Here m = 2, n = 3. Step 3: x-coordinate. x = (2×11 + 3×5)/(2+3) = (22 + 15)/5 = 37/5 Step 4: y-coordinate. y = (2×7 …
Why does putting m = n in the section formula give the midpoint?
Answer
Step 1: Start with the section formula. P = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)) Step 2: Put m = n. P = ((mx2 + mx1)/(2m), (my2 + my1)/(2m)) Step 3: Cancel m from numerator and denominator. P = ((x1…
When do you use the section formula? Show one quick example.
Answer
Use it when a point divides a line segment internally in a given ratio. Formula: x=(mx2+nx1)/(m+n), y=(my2+ny1)/(m+n) Example: For A(2, 1), B(8, 7), ratio 1:1. P = ((1×8 + 1×2)/2, (1×7 + 1×1)/2) P = (…
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