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Mathematics

ABC is a triangle whose vertices are A(1, -1), B(0, 4) and C(-6, 4), D is the mid-point of BC. Find the :

(a) coordinates of D.

(b) equation of the median AD.

Section Formula

ICSE 2023

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Answer

(a) By formula,

Mid-point (M) = (x1+x22,y1+y22)\Big(\dfrac{x1 + x2}{2}, \dfrac{y1 + y2}{2}\Big)

ABC is a triangle whose vertices are A(1, -1), B(0, 4) and C(-6, 4), D is the mid-point of BC. Find the : ICSE 2023 Maths Solved Question Paper.

Given,

D is the mid-point of BC.

∴Co-ordinates of D=(0+(−6)2,4+42)=(−62,82)=(−3,4).\therefore \text{Co-ordinates of D} = \Big(\dfrac{0 + (-6)}{2}, \dfrac{4 + 4}{2}\Big) \\[1em] = \Big(\dfrac{-6}{2}, \dfrac{8}{2}\Big) \\[1em] = (-3, 4).

Hence, co-ordinates of D = (-3, 4).

(b) By two-point form :

Equation of a line :

y - y1 = y2−y1x2−x1(x−x1)\dfrac{y2 - y1}{x2 - x1}(x - x_1)

Substituting values we get :

Equation of AD :

⇒ y - (-1) = 4−(−1)(−3)−1(x−1)\dfrac{4 - (-1)}{(-3) - 1}(x - 1)

⇒ y + 1 = 5−4(x−1)\dfrac{5}{-4}(x - 1)

⇒ -4(y + 1) = 5(x - 1)

⇒ -4y - 4 = 5x - 5

⇒ 5x + 4y = -4 + 5

⇒ 5x + 4y = 1.

Hence, equation of median AD is 5x + 4y = 1.

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