Co-Ordinate Geometry
NIOS · Class 10 · Maths
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What are the coordinates of point P if it is 3 units to the right of y-axis and 4 units above x-axis?
In which quadrant does the point (-5, 7) lie?
Find the distance between points A(0, 0) and B(3, 4).
What is the midpoint of the line segment joining points P(2, 6) and Q(8, 4)?
Sample Questions
If a point lies on the x-axis, what is its y-coordinate?
Find the centroid of triangle with vertices A(0, 0), B(6, 0), and C(3, 6).
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(3, 2)
Step 1: Use centroid formula: G = ((x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3). Step 2: Substitute coordinates: G = ((0+6+3)/3, (0+0+6)/3). Step 3: Calculate: G = (9/3, 6/3) = (3, 2). Step 4: The centroid divides each median in ratio 2:1 from vertex.
Which point divides the line segment joining A(1, 2) and B(7, 8) in the ratio 1:2?
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(3, 4)
Step 1: Use section formula for ratio m:n = 1:2, P = ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n)). Step 2: Substitute: P = ((1×7+2×1)/(1+2), (1×8+2×2)/(1+2)). Step 3: Calculate: P = ((7+2)/3, (8+4)/3) = (9/3, 12/3). Step 4: Therefore P = (3, 4).
The distance between points (a, 0) and (0, a) is:
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a√2
Step 1: Use distance formula d = √[(x₂-x₁)² + (y₂-y₁)²]. Step 2: Substitute: d = √[(0-a)² + (a-0)²] = √[(-a)² + a²]. Step 3: Simplify: d = √[a² + a²] = √(2a²). Step 4: Therefore d = a√2. This forms an isosceles right triangle with the origin.
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