What shape is formed by the points A(-5,1), B(0,3) and C(2,1)?
A Square
B Triangle
C Trapezoid
D Circle
B Triangle
To determine the shape formed by the points A(-5,1), B(0,3), and C(2,1), we can look at the sides and angles of the triangle.
1. Calculate the lengths of each side:
Side AB: √( (0 - (-5))^2 + (3 - 1)^2 ) = √(5^2 + 2^2) = √29
Side BC: √( (2 - 0)^2 + (1 - 3)^2 ) = √(2^2 + (-2)^2) = √8 = 2√2
Side AC: √( (2 - (-5))^2 + (1 - 1)^2 ) = √(7^2 + 0^2) = 7
2. Calculate the angles between the sides:
Angle A: acos( (7^2 + (√29)^2 - (2√2)^2) / (2 * 7 * √29) ) = acos( (49 + 29 - 8) / (2 * 7 * √29) ) = acos(70 / (14√29) )
Angle B: acos( (7^2 + (2√2)^2 - (√29)^2) / (2 * 7 * 2√2) ) = acos( (49 + 8 - 29) / (2 * 7 * 2√2) ) = acos(28 / (28√2) )
Angle C: acos( ((√29)^2 + (2√2)^2 - 7^2) / (2 * √29 * 2√2) ) = acos( (29 + 8 - 49) / (2 √29 * 2√2) ) = acos(-12 / (4√58) )
3. Classify the triangle based on the side lengths and angles:
Using the side lengths, we can see that no two sides have the same length, so it is not an equilateral triangle.
Using the angles, we can see that none of the angles are 90 degrees, so it is not a right angle triangle.
Using the side lengths and angles, we can conclude that the triangle does not meet the criteria to classify it as a specific shape such as a square or a trapezoid.
Therefore, the shape formed by the points A(-5,1), B(0,3), and C(2,1) is a triangle.
The answer is B. Triangle.
To determine the shape formed by the given points A(-5,1), B(0,3), and C(2,1), we can use the concept of geometry and the properties of shapes.
First, let's plot the given points on a coordinate plane.
A(-5,1) is the point with x-coordinate -5 and y-coordinate 1.
B(0,3) is the point with x-coordinate 0 and y-coordinate 3.
C(2,1) is the point with x-coordinate 2 and y-coordinate 1.
Plotting these points will give us a clear visualization.
Now, with the points plotted, we can identify the shape formed by connecting the points.
In this case, when we connect the points A, B, and C, we see that we have a triangle.
Therefore, the correct option is B) Triangle.