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Mathematics

Find :

(i) equation of AB

(ii) equation of CD

Find (i) equation of AB (ii) equation of CD. Equation of a Line, Concise Mathematics Solutions ICSE Class 10.

Straight Line Eq

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Answer

(i) By formula,

Slope = y2−y1x2−x1\dfrac{y2 - y1}{x2 - x1}

Substituting values we get,

Slope of AB =3−43−(−5)=−18.\text{Slope of AB } = \dfrac{3 - 4}{3 - (-5)} \\[1em] = -\dfrac{1}{8}.

By point-slope form,

Equation of AB is :

⇒ y - y1 = m(x - x1)

⇒ y - 4 = −18[x−(−5)]-\dfrac{1}{8}[x - (-5)]

⇒ 8(y - 4) = -1(x + 5)

⇒ 8y - 32 = -x - 5

⇒ x + 8y = -5 + 32

⇒ x + 8y = 27.

Hence, equation of AB is x + 8y = 27.

(ii) From part (i) above,

Slope of AB (m1) = −18-\dfrac{1}{8}

Let slope of CD be m2.

Since, AB ⊥ CD.

∴ m1 × m2 = -1

⇒ −18×m2=−1-\dfrac{1}{8} \times m_2 = -1

⇒ m2=8m_2 = 8.

From figure,

D = (-3, 0)

By point-slope form,

Equation of CD is :

⇒ y - y1 = m(x - x1)

⇒ y - 0 = 8[x - (-3)]

⇒ y = 8(x + 3)

⇒ y = 8x + 24.

Hence, equation of CD is y = 8x + 24.

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