Geometry And Algebra
Kerala Board · Class 10 · Mathematics
Flashcards for Geometry And Algebra — Kerala Board Class 10 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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How do you find the fourth vertex of a parallelogram when three vertices are given: A(3, 2), B(4, 5), and C(6, 3)?
Answer
Step 1: In a parallelogram, opposite sides are equal and parallel. Step 2: Let the fourth vertex be D(x, y). Step 3: For ABCD to be a parallelogram, AB = DC and AD = BC. Step 4: Using the property tha…
What is the formula for finding the midpoint of a line segment joining points (x₁, y₁) and (x₂, y₂)?
Answer
Formula: Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2) Explanation: - The x-coordinate of midpoint is the average of x-coordinates - The y-coordinate of midpoint is the average of y-coordinates Example: Mid…
Find the coordinates of the point that divides the line joining A(2, 4) and B(8, 7) in the ratio 1:2.
Answer
Step 1: Let P divide AB in ratio 1:2, so AP:PB = 1:2 Step 2: This means AP = 1/3 of AB Step 3: Change in coordinates from A to B: Δx = 8 - 2 = 6 Δy = 7 - 4 = 3 Step 4: Change from A to P = 1/3 o…
What is the slope of a line and how do you calculate it from two points?
Answer
Definition: Slope is the measure of steepness of a line. Formula: Slope (m) = (y₂ - y₁)/(x₂ - x₁) Where (x₁, y₁) and (x₂, y₂) are two points on the line. Example: Slope of line through (2, 3) and (…
Find the equation of the line passing through (2, 4) with slope 3/2.
Answer
Step 1: Use point-slope form: y - y₁ = m(x - x₁) Step 2: Given: (x₁, y₁) = (2, 4) and m = 3/2 Step 3: Substitute in formula: y - 4 = (3/2)(x - 2) Step 4: Simplify: y - 4 = (3/2)x - 3 y = (3/2…
How do you prove that three points are collinear (lie on the same line)?
Answer
Method 1: Using Slope Step 1: Calculate slope of line joining first two points Step 2: Calculate slope of line joining second and third points Step 3: If slopes are equal, points are collinear Method…
What is the equation of a circle with center (h, k) and radius r?
Answer
Standard Form: (x - h)² + (y - k)² = r² Where: - (h, k) is the center of the circle - r is the radius Example: Circle with center (3, -2) and radius 5 (x - 3)² + (y - (-2))² = 5² (x - 3)² + (y + 2)²…
Find the center and radius of the circle x² + y² - 4x + 6y - 12 = 0.
Answer
Step 1: Rearrange equation to group x and y terms x² - 4x + y² + 6y = 12 Step 2: Complete the square for x terms: x² - 4x = (x - 2)² - 4 Step 3: Complete the square for y terms: y² + 6y = (y …
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Sources & Official References
- Kerala Board of Public Examinations — keralapareekshabhavan.in
- National Education Policy 2020 — education.gov.in
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