Mathematics - For Class IX (Science Group) - Comprehensive Paper 2024 - By Practical Center

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Class IX (Science)
Mathematics I
Comprehensive Paper 2024

By Practical Center

Solved By Ustani G (Education Center)
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SECTION 'B'
Short Answer-Questions

SECTION 'C'
Descriptive Answer-Questions

Q.15: Take a △ and draw the altitudes and prove that they are concurrent (and also write steps of construction).
Solution:

Steps Of Construction:

1. Draw a triangle ABC.
2. Take point A as a center and draw an arc of suitable radius, which cuts BC at point D and E.
3. From D as a center, draw an arc of radius more than the ½ of m DE.
4. Again from point E draw another arc of same radius, cutting first arc at point F.
5. Join point A and F. Such that AF intersect BC at point P.
6. Then AP is the altitude of △ABC from the vertex A.
7. Repeat the steps (ii) to (v) and draw BQ and CR, the altitudes of △ABC from the vertices B and C respectively.
8. Hence AP, BQ and CR are required altitudes of △ABC.

Q.16: Find the perimeter of the triangle formed by the point A(0, 0), B(4, 0) and C(2, 2√3)
Solution:
A = (0, 0)
B = (4, 0)
C = (2, 2√3)

⇒ |AB| = |BC|= |AC|
⇒ |AB|  = A = (0, 0) (x₁, y₁)
⇒  |AB| = B = (4, 0) (x₂, y₂)

By using distance formula:

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