A triangle is graphed in the coordinate plane. The vertices of the triangle have coordinates (5, 1), (1, 1), and (1, 7). What is the perimeter of the triangle?
28
24
14---- my answer
10
Correcto Dude
you have a right triangle with legs 4 and 6. The hypotenuse is thus 2√13.
I don't see any good choices.
good job
To find the perimeter of a triangle, you need to calculate the sum of the lengths of all its sides.
To calculate the length of a side, you can use the distance formula. The distance formula gives us the distance between two points in a coordinate plane.
The formula is:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the lengths of the sides:
1. The distance between (5, 1) and (1, 1) is:
distance = sqrt((1 - 5)^2 + (1 - 1)^2) = sqrt(16 + 0) = sqrt(16) = 4
2. The distance between (1, 1) and (1, 7) is:
distance = sqrt((1 - 1)^2 + (7 - 1)^2) = sqrt(0 + 36) = sqrt(36) = 6
3. The distance between (1, 7) and (5, 1) is:
distance = sqrt((5 - 1)^2 + (1 - 7)^2) = sqrt(16 + 36) = sqrt(52) = 2 * sqrt(13)
Now, let's calculate the perimeter by adding up the lengths of all sides:
Perimeter = 4 + 6 + 2 * sqrt(13)
Using a calculator, the approximate value of the perimeter is 14.68.
Therefore, the closest option to the actual perimeter of the triangle is 14. Thus, the correct answer is 14.