Co-Ordinate Geometry
NIOS · Class 10 · Maths
Flashcards for Co-Ordinate Geometry — NIOS Class 10 Maths. Quick Q&A cards covering key concepts, definitions, and formulas.
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See them allFind the distance between points A(3, 4) and B(6, 8).
Answer
Step 1: Use distance formula d = √[(x₂-x₁)² + (y₂-y₁)²] Step 2: Identify coordinates: A(3,4) → x₁=3, y₁=4; B(6,8) → x₂=6, y₂=8 Step 3: Substitute: d = √[(6-3)² + (8-4)²] Step 4: Calculate: d = √[3² + …
Find the coordinates of the midpoint of line segment joining P(-2, 3) and Q(4, -1).
Answer
Step 1: Use midpoint formula: M = ((x₁+x₂)/2, (y₁+y₂)/2) Step 2: Identify coordinates: P(-2,3) → x₁=-2, y₁=3; Q(4,-1) → x₂=4, y₂=-1 Step 3: Calculate x-coordinate: x = (-2+4)/2 = 2/2 = 1 Step 4: Calcu…
A point P divides the line segment joining A(1, 2) and B(7, 8) in the ratio 2:1 internally. Find the coordinates of P.
Answer
Step 1: Use section formula: P = ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n)) Step 2: Given: A(1,2), B(7,8), ratio m:n = 2:1 Step 3: Calculate x-coordinate: x = (2×7 + 1×1)/(2+1) = (14+1)/3 = 15/3 = 5 Step 4: C…
Find the centroid of triangle with vertices A(2, 3), B(-4, 1), and C(6, -5).
Answer
Step 1: Use centroid formula: G = ((x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3) Step 2: Identify coordinates: A(2,3), B(-4,1), C(6,-5) Step 3: Calculate x-coordinate: x = (2+(-4)+6)/3 = 4/3 Step 4: Calculate y-coordin…
The distance between points (0, 0) and (x, 4) is 5 units. Find the value of x.
Answer
Step 1: Use distance formula: d = √[(x₂-x₁)² + (y₂-y₁)²] Step 2: Substitute given values: 5 = √[(x-0)² + (4-0)²] Step 3: Simplify: 5 = √[x² + 16] Step 4: Square both sides: 25 = x² + 16 Step 5: Solve:…
Which quadrant does the point P(-3, 7) lie in?
Answer
Step 1: Identify the signs of coordinates: x = -3 (negative), y = 7 (positive) Step 2: Remember quadrant rules: - Quadrant I: (+,+) - Quadrant II: (-,+) - Quadrant III: (-,-) - Quadrant IV: (+,-) Step…
Find the distance of point A(5, -12) from the origin.
Answer
Step 1: Origin is at O(0, 0) Step 2: Use distance formula: d = √[(x₂-x₁)² + (y₂-y₁)²] Step 3: Substitute: d = √[(5-0)² + (-12-0)²] Step 4: Calculate: d = √[25 + 144] = √169 = 13 Answer: 13 units…
Show that points A(1, 1), B(2, 3), and C(3, 5) are collinear.
Answer
Step 1: Find distances AB, BC, and AC Step 2: AB = √[(2-1)² + (3-1)²] = √[1+4] = √5 Step 3: BC = √[(3-2)² + (5-3)²] = √[1+4] = √5 Step 4: AC = √[(3-1)² + (5-1)²] = √[4+16] = √20 = 2√5 Step 5: Check if…
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