Coordinate Geometry — Flashcards
Tamil Nadu Board · Class 9 · Mathematics
25 flashcards for Coordinate Geometry (Tamil Nadu Board Class 9 Mathematics) to test yourself on key terms and facts.
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Identify the quadrant: Point (3, -8)
Answer
Step 1: Check the sign of x-coordinate: x = 3 (positive) Step 2: Check the sign of y-coordinate: y = -8 (negative) Step 3: Since x > 0 and y < 0, the point lies in Quadrant IV Answer: Quadrant IV Rem…
Plot the point (-3, 5) on a Cartesian plane. Which quadrant does it lie in?
Answer
Step 1: Start at origin O(0,0) Step 2: Move 3 units to the left (negative x-direction) Step 3: Move 5 units upward (positive y-direction) Step 4: Mark the intersection point at (-3, 5) Step 5: Check s…
Find the distance between points A(1, 2) and B(4, 3)
Answer
Using Distance Formula: d = √[(x₂ - x₁)² + (y₂ - y₁)²] Step 1: Identify coordinates: (x₁,y₁) = (1,2), (x₂,y₂) = (4,3) Step 2: Apply formula: d = √[(4-1)² + (3-2)²] Step 3: Calculate: d = √[3² + 1²] S…
Calculate the distance between (-4, 3) and (2, -3)
Answer
Using Distance Formula: d = √[(x₂ - x₁)² + (y₂ - y₁)²] Step 1: Identify: (x₁,y₁) = (-4,3), (x₂,y₂) = (2,-3) Step 2: Substitute: d = √[(2-(-4))² + (-3-3)²] Step 3: Simplify inside brackets: d = √[(2+4…
When do you use the distance formula? Give an example of a real-world situation
Answer
Use the distance formula when you need to: 1. Find the straight-line distance between two points 2. Check if points form geometric shapes (triangle, square, etc.) 3. Determine if three points are coll…
Are the points A(3, 1), B(6, 4), and C(8, 6) collinear?
Answer
Method: Three points are collinear if AB + BC = AC Step 1: Calculate AB = √[(6-3)² + (4-1)²] AB = √[9 + 9] = √18 = 3√2 Step 2: Calculate BC = √[(8-6)² + (6-4)²] BC = √[4 + 4] = √8 = 2√…
Find the midpoint of the line segment joining A(-8, -10) and B(4, -2)
Answer
Using Midpoint Formula: M = ((x₁+x₂)/2, (y₁+y₂)/2) Step 1: Identify coordinates: (x₁,y₁) = (-8,-10), (x₂,y₂) = (4,-2) Step 2: Calculate x-coordinate of midpoint: x = (-8 + 4)/2 = -4/2 = -2 Ste…
The center of a circle is (3, -4). If one end of the diameter is (5, -6), find the other end
Answer
Key concept: Center is the midpoint of diameter Using: Center = ((x₁+x₂)/2, (y₁+y₂)/2) Step 1: Let other end be B(x₂, y₂). Given: Center (3, -4), A(5, -6) Step 2: For x-coordinate: 3 = (5 + x₂)/2 …
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