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ICSE Class X Mid-term 2026 : Biology

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Official Answer Key & Marking Scheme Mathematics Class X Section Formula & Coordinate Geometry MAX MARKS: 04 y QUESTION 1 (4 MARKS) B P In the given figure, line APB meets the x-axis at point A and y-axis at point B. P is the point ( 4, 2) and AP : PB = 1 : 2. Find the co-ordinates of A and B. A Step Mathematical Working & Deductions 1. Coordinate Let A on the x-axis be (x, 0) and B on the y-axis be (0, y). Identification Given: P( 4, 2) and ratio AP : PB = m1 : m2 = 1 : 2. 2. Section Formula Formulation By section formula for internal division: xp = x O Marks m1 x 2 + m2 x 1 m1 y 2 + m2 y 1 m1 + m2 1M , yp = 1M m1 + m2 3. Evaluation of Point A Substitute xp = 4, x1 = x, x2 = 0: 1M Substitute yp = 2, y1 = 0, y2 = y: 1M 1(0) + 2(x) 2x 4 = 4 = 2x = 12 x = 6. Hence A( 6, 0). 1+2 3 4. Evaluation of Point B 1(y) + 2(0) y 2= 2= y = 6. Hence B(0, 6). 1+2 3 Method A: Standard Ratio (m : m ) Direct Evaluation Set m1 = 1 and m2 = 2: x-coordinate: 4 = [1(0) + 2(x)] / 3 2x = 12 x = 6 y-coordinate: 2 = [1(y) + 2(0)] / 3 y = 6 Provides immediate cross-multiplication with integer values. FINAL VERIFIED COORDINATES Points lying on respective coordinate axes Secondary Mathematics Examination Evaluation Scheme Method B: k : 1 Ratio Method Let ratio be k : 1 where k = Fractional k Form 1 : 2 1 2x + 1] = x = 6 2 3 1 1 y y-coordinate: 2 = [ (y) + 0] / [ + 1] = y=6 2 2 3 1 2 x-coordinate: 4 = [ (0) + x] / [ Validates consistency with parameterized ratio models. A = ( 6, 0) | B = (0, 6) Page 1 of 1

 

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