Find the coordinates of the midpoint of the segment with the given endpoints G(-4, 4) and H(6, 4).

Solution:

Coordinate Geometry is one of the most important branches in mathematics which has an immense number of applications in various fields of engineering and science. This branch of maths deals with the representation of curves on the coordinate plane. 

Let's understand the solution in detail.

We use the section formula to solve the problem.

Let's understand the section formula using the diagram given below.

From the above figure, we can see that if P divides the line segment AB in the ratio m₁:m₂, then coordinates of P is given by the formula:

⇒ x-coordinate of P = (m₁x₂ + m₂x₁) / (m₁ + m₂) ---------------- (1)

⇒ y-coordinate of P = (m₁y₂ + m₂y₁) / (m₁ + m₂) --------------- (2)

In the above problem given, we apply this formula to get the answer.

To find the midpoint, we see that it divides the line segment GH in the ratio 1:1. Hence, m₁ = 1 and m₂ = 1.

Let's substitute the coordinates of G for (x₁, y₁) and coordinates of H for (x₂, y₂) wth m₁ = 1 and m₂ = 1 in (1) and (2)

Hence, The coordinates of the midpoint are given by ((x₁ + x₂) / 2, (y₁ + y₂) / 2).-------------- (3)

We have, G(-4, 4) and H(6, 4) [Given]

Thus, x₁ = -4, x₂ = 6, y₁ = 4, y₂ = 4

By substituting these values in (3) we get,

The coordinates of the midpoint = ((-4 + 6) / 2, (4 + 4) / 2).

The coordinates of the midpoint = (1, 4)

Hence, the coordinates of the midpoint of the segment with the given endpoints G(-4, 4) and H(6, 4) are (1, 4).

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Find the coordinates of the midpoint of the segment with the given endpoints G(-4, 4) and H(6, 4).

Summary:

The coordinates of the midpoint of the segment with the given endpoints G(-4, 4) and H(6, 4) are (1, 4).