Mathematics
Line AB is perpendicular to CD. Coordinates of B, C and D are respectively (4, 0), (0, –1) and (4, 3). Find :
(i) Slope of CD.
(ii) Equation of AB.
Straight Line Eq
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Answer
(i) By formula,
Slope of a line =
Substituting values we get :
Slope of CD =
Hence, slope of CD = 1.
(ii) We know that,
The product of slope of two perpendicular lines equals to -1.
∴ Slope of AB × Slope of CD = -1
⇒ Slope of AB × 1 = -1
⇒ Slope of AB = -1.
By point-slope formula,
Equation of line
⇒ y - y1 = m(x - x1)
Equation of AB :
⇒ y - 0 = -1(x - 4)
⇒ y = -x + 4
⇒ x + y = 4.
Hence, equation of AB is x + y = 4.
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