Find the value of a, if the line passing through
(-5,-8) and (3, 0) is parallel to the line passing
through (6, 3) and (4, a).
Answers
Answer:
The value of a is 2.
Step-by-step-explanation:
Let the given points be A, B, C & D.
We have given that,
A ≡ ( - 5, - 8 ) ≡ ( x₁, y₁ )
B ≡ ( 3, 0 ) ≡ ( x₂, y₂ )
C ≡ ( 6, 3 ) ≡ ( x₃, y₃ )
D ≡ ( 4, a ) ≡ ( x₄, y₄ )
Also,
Lines AB and CD are parallel to each other.
∴ Lines AB & CD have equal slopes.
∴ Slope of line AB = Slope of line CD
⇒ ( y₂ - y₁ ) / ( x₂ - x₁ ) = ( y₄ - y₃ ) / ( x₄ - x₃ )
⇒ [ 0 - ( - 8 ) ] / [ 3 - ( - 5 ) ] = ( a - 4 ) / ( 4 - 6 )
⇒ ( 0 + 8 ) / ( 3 + 5 ) = ( a - 4 ) / ( - 2 )
⇒ 8 / 8 = ( a - 4 ) / ( - 2 )
⇒ 1 = ( a - 4 ) / ( - 2 )
⇒ a - 4 = 1 × ( - 2 )
⇒ a - 4 = - 2
⇒ a = - 2 + 4
⇒ a = 2
∴ The value of a is 2.
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Additional Information:
1. Slope of line:
The ratio of difference between y coordinates and x coordinates is constant and called as slope of the line.
2. It is denoted by the letter m.
3. Slope of X - axis is 0.
4. Slope of Y - axis cannot be determined.
5. Parallel lines have equal slopes.
6. Formula for finding slope of line:
- m = ( y₂ - y₁ ) / ( x₂ - x₁ )