When the coordinates (2, 3), (4, 4), (6, 3), and (4, 2) are joined, which shape is formed?

Solution:

Given, the coordinates are (2, 3), (4, 4), (6, 3), and (4, 2).

We have to find the shape formed by joining the coordinates.

Let the coordinates A(2,3); B(4,4); C(6,3) and D(4,2)

The distance between the coordinates can be found by using the formula

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

The distance between the coordinates A(2,3) and B(4,4)

AB = √[(4 - 2)² + (4 - 3)²

AB = √(4 + 1)

AB = √5

The distance between the coordinates B(4,4) and C(6,3)

BC = √[(6 - 4)² + (3 - 4)²]

BC = √(4 + 1)

BC = √5

The distance between the coordinates C(6,3) and D(4,2)

CD = √[(4 - 6)² + (2 - 3)²]

CD = √(4 + 1)

CD = √5

The distance between the coordinates D(4,2) and A(2,3)

DA = √[(2 - 4)² + (3 - 2)²]

DA = √(4 + 1)

DA = √5

So, AB = BC = CD = DA 

The slope of opposite sides AB and CD are

AB = m = (y₂ - y₁)/(x₂ - x₁)

m = (4 - 3) / (4 - 2)

m = 1/2

CD = m = (2 - 3)/ (4 - 6)

m = -1 / -2

m = 1/2

So the slopes of opposite sides are equal.

Therefore, the shape formed by joining the given coordinates is rhombus.

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When the coordinates (2, 3), (4, 4), (6, 3), and (4, 2) are joined, which shape is formed?

Summary:

When the coordinates (2, 3), (4, 4), (6, 3), and (4, 2) are joined, the shape formed is rhombus.