1.A triangle has three vertexes. Point A is (0,0) point B is (4,10) and point C is (8,0). What are the lengths of each side?
2. What is halfway between -2 and 1?
To find the lengths of the sides of the triangle described in question 1, we can use the distance formula. The distance formula is derived from the Pythagorean theorem and calculates the distance between two points in a coordinate plane.
1. Triangle ABC:
- Side AB: To find the length of side AB, we use the distance formula, which is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using the coordinates (0,0) for point A and (4,10) for point B, the formula becomes:
AB = sqrt((4 - 0)^2 + (10 - 0)^2)
= sqrt(16 + 100)
= sqrt(116)
≈ 10.77 (rounded to two decimal places)
- Side BC: The length of side BC can also be found using the distance formula, using the coordinates (4,10) for point B and (8,0) for point C:
BC = sqrt((8 - 4)^2 + (0 - 10)^2)
= sqrt(16 + 100)
= sqrt(116)
≈ 10.77 (rounded to two decimal places)
- Side CA: Finally, the length of side CA can be found using the distance formula, using the coordinates (8,0) for point C and (0,0) for point A:
CA = sqrt((8 - 0)^2 + (0 - 0)^2)
= sqrt(64 + 0)
= sqrt(64)
= 8
Therefore, the lengths of the sides of the triangle ABC are approximately 10.77, 10.77, and 8 (rounded to two decimal places).
2. To find the number halfway between -2 and 1, you can calculate the average of these two numbers. The average (or mean) of two numbers is found by adding them together and dividing the sum by 2.
Average = (Number1 + Number2) / 2
In this case, the numbers are -2 and 1:
Average = (-2 + 1) / 2
= -1 / 2
= -0.5
Therefore, the number halfway between -2 and 1 is -0.5.