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Question
What is the perimeter of triangle A B Cwith vertices A left-parenthesis negative 2 comma 9 right-parenthesis, B left-parenthesis 7 comma negative 3 right-parenthesis, and C left-parenthesis negative 2 comma negative 3 right-parenthesis in the coordinate plane?
(1 point)
Responses
21 units
21 units
15 units
15 units
34 units
34 units
36 units
To find the perimeter of a triangle, we need to find the distance between each pair of vertices and then sum them up.
The distance between points A(-2,9) and B(7,-3) can be found using the distance formula: d = √((x2 - x1)^2 + (y2 - y1)^2)
d = √((7 - (-2))^2 + (-3 - 9)^2) = √((9)^2 + (-12)^2) = √(81 + 144) = √225 = 15
The distance between points B(7,-3) and C(-2,-3) can be found using the distance formula: d = √((x2 - x1)^2 + (y2 - y1)^2)
d = √((-2 - 7)^2 + (-3 - (-3))^2) = √((-9)^2 + (0)^2) = √(81 + 0) = √81 = 9
The distance between points C(-2,-3) and A(-2,9) can be found using the distance formula: d = √((x2 - x1)^2 + (y2 - y1)^2)
d = √((-2 - (-2))^2 + (9 - (-3))^2) = √((0)^2 + (12)^2) = √(0 + 144) = √144 = 12
Now, let's find the perimeter by summing up the distances:
Perimeter = 15 + 9 + 12 = 36
Therefore, the perimeter of triangle ABC is 36 units. The correct answer is 36 units.
To find the perimeter of triangle ABC, we need to find the lengths of the three sides and then add them together.
Step 1: Find the length of side AB.
Using the distance formula, we can find the distance between points A and B.
distance = √((x2 - x1)^2 + (y2 - y1)^2)
distance = √((7 - (-2))^2 + (-3 - 9)^2) = √((7 + 2)^2 + (-3 - 9)^2)
distance = √((9)^2 + (-12)^2) = √(81 + 144) = √225 = 15 units
Step 2: Find the length of side BC.
Using the distance formula, we can find the distance between points B and C.
distance = √((x2 - x1)^2 + (y2 - y1)^2)
distance = √((-2 - 7)^2 + (-3 - (-3))^2) = √((-2 - 7)^2 + (0)^2)
distance = √((-9)^2 + 0) = √(81 + 0) = √81 = 9 units
Step 3: Find the length of side AC.
Using the distance formula, we can find the distance between points A and C.
distance = √((x2 - x1)^2 + (y2 - y1)^2)
distance = √((-2 - (-2))^2 + (-3 - 9)^2) = √((-2 + 2)^2 + (-3 - 9)^2)
distance = √((0)^2 + (-12)^2) = √(0 + 144) = √144 = 12 units
Step 4: Calculate the perimeter.
The perimeter is the sum of the lengths of all three sides.
perimeter = 15 + 9 + 12 = 36 units
Therefore, the perimeter of triangle ABC is 36 units.
To find the perimeter of triangle ABC with the given vertices, you can use the distance formula to calculate the length of each side. The distance formula is derived from the Pythagorean theorem and finds the distance between two points in a coordinate plane.
The distance formula is:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the lengths of the sides:
1. Side AB:
Using the distance formula, we have:
dAB = sqrt((7 - (-2))^2 + (-3 - 9)^2) = sqrt(9^2 + (-12)^2) = sqrt(81 + 144) = sqrt(225) = 15
2. Side BC:
Using the distance formula, we have:
dBC = sqrt((-2 - 7)^2 + (-3 - (-3))^2) = sqrt((-9)^2 + 0^2) = sqrt(81 + 0) = sqrt(81) = 9
3. Side AC:
Using the distance formula, we have:
dAC = sqrt((-2 - (-2))^2 + (9 - (-3))^2) = sqrt(0^2 + 12^2) = sqrt(0 + 144) = sqrt(144) = 12
Now, add up the lengths of all three sides to find the perimeter of triangle ABC:
Perimeter = AB + BC + AC = 15 + 9 + 12 = 36 units
Therefore, the correct answer is 36 units.