Question 5 Find the slope of a line, which passes through the origin, and the mid-point of
the line segment joining the points P (0, –4) and B (8, 0).
Class X1 - Maths -Straight Lines Page 211
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P ( 0, - 4) and Q ( 8, 0)
we know,
mid point of two points (x₁,y₁) and (x₂,y₂) is
= {(x₁ + x₂)/2, (y₁ + y₂)/2 }
={ ( 0 + 8)/2 , ( -4 + 0)/2 }
= ( 4 , -2 )
now, slope of line passing through origin and (4,-2) is m = (y₂ - y₁)/(x₂ - x₁)
= (-2 - 0)/(4 - 0)
= -2/4
= -1/2
hence, slope of line is -1/2
we know,
mid point of two points (x₁,y₁) and (x₂,y₂) is
= {(x₁ + x₂)/2, (y₁ + y₂)/2 }
={ ( 0 + 8)/2 , ( -4 + 0)/2 }
= ( 4 , -2 )
now, slope of line passing through origin and (4,-2) is m = (y₂ - y₁)/(x₂ - x₁)
= (-2 - 0)/(4 - 0)
= -2/4
= -1/2
hence, slope of line is -1/2
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