What is the perimeter, in units, of ΔABC with A(−1,−6), B(7,−6), and C(3,−3)?
12 units
14 units,
16 units,
18 units,
I think its 16
Note that it is an isosceles triangle with
AB = 8
BC=AC = 5
So add 'em up to get 18
Well, you might be right! But let's have a little bit of mathematical clowning to find out.
To find the perimeter of a triangle, we need to find the distance between each pair of points and add them up.
The distance between A(-1, -6) and B(7, -6) is 8 units.
The distance between B(7, -6) and C(3, -3) is √((7-3)² + (-6-(-3))²) = √16 + 9 = √25 = 5 units.
The distance between C(3, -3) and A(-1, -6) is √((3-(-1))² + (-3-(-6))²) = √16 + 9 = √25 = 5 units.
Now, let's add 'em up: 8 + 5 + 5 = 18 units.
So, the correct answer is 18 units. I hope my little clown act didn't confuse you too much!
To find the perimeter of triangle ABC, you need to calculate the distance between each pair of points and sum them up.
The distance formula between two points (x1, y1) and (x2, y2) is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the distances between each pair of points:
AB = √((7 - (-1))^2 + (-6 - (-6))^2) = √(8^2 + 0^2) = √(64 + 0) = √64 = 8
AC = √((3 - (-1))^2 + (-3 - (-6))^2) = √(4^2 + 3^2) = √(16 + 9) = √25 = 5
BC = √((7 - 3)^2 + (-6 - (-3))^2) = √(4^2 + 3^2) = √(16 + 9) = √25 = 5
Now, add up the three distances to get the perimeter:
Perimeter = AB + AC + BC = 8 + 5 + 5 = 18
So, the perimeter of triangle ABC is 18 units.
To find the perimeter of a triangle, you need to calculate the sum of the lengths of its sides.
In this case, you have the coordinates of three points: A(-1,-6), B(7,-6), and C(3,-3).
To find the length of each side, you can use the distance formula, which states that the distance between two points (x1, y1) and (x2, y2) is given by the formula sqrt((x2 - x1)^2 + (y2 - y1)^2).
Let's calculate the lengths of the sides of triangle ABC:
Length of side AB:
sqrt((7 - (-1))^2 + (-6 - (-6))^2)
= sqrt(8^2)
= sqrt(64)
= 8 units
Length of side BC:
sqrt((3 - 7)^2 + (-3 - (-6))^2)
= sqrt((-4)^2 + 3^2)
= sqrt(16 + 9)
= sqrt(25)
= 5 units
Length of side AC:
sqrt((-1 - 3)^2 + (-6 - (-3))^2)
= sqrt((-4)^2 + (-3)^2)
= sqrt(16 + 9)
= sqrt(25)
= 5 units
Now, you can add up the lengths of the three sides to find the perimeter:
Perimeter = Length of AB + Length of BC + Length of AC
= 8 + 5 + 5
= 18 units
So, the perimeter of triangle ABC is 18 units. Therefore, the correct answer from the given options is 18 units.