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The points A (x₁, y₁), B (x₂, y₂) and C (x₃, y₃) are the vertices of ∆ ABC. The median from A meets BC at D. Find the coordinates of the point D

Solution:

Given, the vertices of the triangle ABC are A(x₁, y₁), B (x₂, y₂) and C (x₃, y₃)

The median from A meets BC at D.

We have to find the coordinates of point D.

Since, median AD meets BC at D. D bisects BC into two equal parts.

i.e., BC = BD + DC

So, D is the midpoint of BC.

We know that the coordinates of the mid-point of the line segment joining the points P (a , b) and Q (c , d) are [(a + c)/2, (b + d)/2]

Midpoint of B(x₂, y₂) and C (x₃, y₃) = D

D = [(x₂ + x₃)/2, (y₂ + y₃)/2]

Therefore, the coordinates of D are (x₂ + x₃)/2 and (y₂ + y₃)/2.

✦ Try This: A (4, 2), B(6, 5) and C(1, 4) be the vertices of ∆ABC. The median from A meets BC at D. Find the coordinates of the point D.

Given, the vertices of the triangle ABC are A(4, 2) B(6, 5) and C(1, 4).

The median from A meets BC at D.

We have to find the coordinates of point D.

Since, median AD meets BC at D. D bisects BC into two equal parts.

i.e., BC = BD + DC

So, D is the midpoint of BC.

Midpoint of B(6, 5) and C(1, 4) = D

D = [(6 + 1)/2, (5 + 4)/2]

D = [7/2, 9/2]

Therefore, the coordinates of D are 7/2 and 9/2.

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 7

NCERT Exemplar Class 10 Maths Exercise 7.4 Problem 3(i)

The points A (x₁, y₁), B (x₂, y₂) and C (x₃, y₃) are the vertices of ∆ ABC. The median from A meets BC at D. Find the coordinates of the point D

Summary:

The points A (x₁, y₁), B (x₂, y₂) and C (x₃, y₃) are the vertices of ∆ ABC. The median from A meets BC at D. The coordinates of the point D are (x₂+x₃)/2 and (y₂+y₃)/2

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