identify the figure with the vertices A (3,5) B (3,1) C (0,1)

Answer:

It makes a right traiangle.

Step-by-step explanation:

Graph the points and you will see that it makes a right triangle.

The figure formed by the vertices A(3,5), B(3,1), and C(0,1) is a right-angled triangle.

In this triangle, side BC is the shortest side with a length of 3 units, side AB is the longest side with a length of 4 units, and side AC has a length of 5 units.

The right angle is formed between side BC and side AC at point C (0,1).

Here, we have to identify the figure with the given vertices A (3,5), B (3,1), and C (0,1), we can plot these points on a coordinate plane.

Let's plot the points A(3,5), B(3,1), and C(0,1) on a Cartesian coordinate plane.

A(3,5): This point is located at x-coordinate 3 and y-coordinate 5.

B(3,1): This point is located at x-coordinate 3 and y-coordinate 1.

C(0,1): This point is located at x-coordinate 0 and y-coordinate 1.

Since point A and point B share the same x-coordinate (x = 3), they lie on a vertical line. Point C has a different x-coordinate, so we need to connect it with the others to complete the figure.

The figure formed by connecting the points A, B, and C is a right-angled triangle.

To calculate the distances between the vertices, we'll use the distance formula:

Distance between two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given by:

Distance = √[tex]((x_2 - x_1)^2 + (y_2 - y_1)^2)[/tex]

Let's calculate the distances:

Distance between A(3,5) and B(3,1):

Distance_AB = √[tex]((3 - 3)^2 + (1 - 5)^2)[/tex]

Distance_AB = √(0 + 16)

Distance_AB = √16

Distance_AB = 4 units

Distance between A(3,5) and C(0,1):

Distance_AC = √[tex]((0 - 3)^2 + (1 - 5)^2)[/tex]

Distance_AC = √[tex]((-3)^2 + (-4)^2)[/tex]

Distance_AC = √(9 + 16)

Distance_AC = √25

Distance_AC = 5 units

Distance between B(3,1) and C(0,1):

Distance_BC = √[tex]((0 - 3)^2 + (1 - 1)^2)[/tex]

Distance_BC = √[tex]((-3)^2 + 0^2)[/tex]

Distance_BC = √9

Distance_BC = 3 units

As we calculated, the distances between the vertices of the figure are:

AB = 4 units

AC = 5 units

BC = 3 units

Based on the distances, we can determine that the figure formed by the vertices A(3,5), B(3,1), and C(0,1) is a right-angled triangle.

In this triangle, side BC is the shortest side with a length of 3 units, side AB is the longest side with a length of 4 units, and side AC has a length of 5 units.

The right angle is formed between side BC and side AC at point C (0,1).

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