Question

A (3,4),B(3,5),C(3,7) then triangle ABC is

Answer 1

Answer:

A (3,4), B(3,5), and C(3,7) does not form a triangle

Step-by-step explanation:

Given

A (3,4), B(3,5), C(3,7)

To find

The type of triangle is formed with the given coordinates

Solution:

Recall the formula,

The distance between two points A(x₁, y₁) and B(x₂, y₂) is given by the formula

AB = $\sqrt{(x_2 - x_1)^2 + (y_2- y_1)^2}$

Since the vertices of the triangle are A (3,4), B(3,5), C(3,7)

The length of the side AB = $\sqrt{(3 - 3)^2 + (5- 4)^2}$

= $\sqrt{0+1}$

= 1 unit

The length of the side BC = $\sqrt{(3 - 3)^2 + (7- 5)^2}$

= $\sqrt{0+4}$

= 2 unit

The length of the side AC = $\sqrt{(3 - 3)^2 + (7- 4)^2}$

= $\sqrt{0+9}$

= 3 unit

Since AB + BC = AC, the three points are collinear. Hence we can conclude that the vertices A, B, and C does not form a triangle.

Alternate method

When we analyze the given three points A (3,4), B(3,5), and C(3,7), we can see that the x - coordinate of all these three points = 3

This means all these points lie on the line x = 3.

Hence these points are collinear and do not form a triangle.

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Answer 2

Answer:

The points A(3,4) B(3,5) and C(3,7) do not form a triangle as considering the x-axis points of all the three points A,B,C, all these points are on the x-axis, and so they are collinear points.

So all the points would be on the same line and they are not the points of a triangle.

Step-by-step explanation:

• Considering the properties of a triangle, a triangle has three sides forming three vertices and three angles
• The sum of the angles of a triangle is always 180 degrees
• Since the triangle has three vertices, the points of a triangle are non - collinear .

Considering the given points, A(3,4) B(3,5) and C(3,7), all these points are on the x-axis, as the x-axis points of all the three points are the same. As these are collinear points, these points are not the points of a triangle,

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