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The perimeter of the triangle formed by the points A(0,0), B(1,0) and C(0,1) is
- a)√2 + 1
- b)1 ± √2
- c)2 + √2
- d)3
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The perimeter of the triangle formed by the points A(0,0), B(1,0) and ...
Consider A (0,0),B (1,0),C (0,1)
=>AB=root(X2-X1)^2+(Y2-Y1)^2
=>AB=root (1-0)^2+(1-0)^2
=>AB=1
similarly,
BC=root2
and
AC=1
Perimeter=AB+BC+AC
=1+root1+1
=2+root2
Most Upvoted Answer
The perimeter of the triangle formed by the points A(0,0), B(1,0) and ...
First of all find the distance using distance formula....and tyen add all the distances for perimeter
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The perimeter of the triangle formed by the points A(0,0), B(1,0) and ...
To find the perimeter of a triangle, we need to find the lengths of all three sides and then add them together. Let's go step by step to find the lengths of the sides of triangle ABC.
First, let's find the distance between points A and B. The distance formula is given by:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
For points A(0,0) and B(1,0), the distance is:
Distance AB = sqrt((1 - 0)^2 + (0 - 0)^2) = sqrt(1 + 0) = 1
Next, let's find the distance between points B and C. Using the distance formula:
Distance BC = sqrt((0 - 1)^2 + (1 - 0)^2) = sqrt(1 + 1) = sqrt(2)
Finally, let's find the distance between points C and A:
Distance CA = sqrt((0 - 0)^2 + (0 - 1)^2) = sqrt(0 + 1) = 1
Now, we have the lengths of all three sides of the triangle: AB = 1, BC = sqrt(2), and CA = 1.
To find the perimeter, we add the lengths of all three sides:
Perimeter = AB + BC + CA
Perimeter = 1 + sqrt(2) + 1
Simplifying the expression, we get:
Perimeter = 2 + sqrt(2)
The exact value of the perimeter is 2 + sqrt(2). However, in the given options, the closest value is 2. Therefore, the correct answer is option C: 2 2.
First, let's find the distance between points A and B. The distance formula is given by:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
For points A(0,0) and B(1,0), the distance is:
Distance AB = sqrt((1 - 0)^2 + (0 - 0)^2) = sqrt(1 + 0) = 1
Next, let's find the distance between points B and C. Using the distance formula:
Distance BC = sqrt((0 - 1)^2 + (1 - 0)^2) = sqrt(1 + 1) = sqrt(2)
Finally, let's find the distance between points C and A:
Distance CA = sqrt((0 - 0)^2 + (0 - 1)^2) = sqrt(0 + 1) = 1
Now, we have the lengths of all three sides of the triangle: AB = 1, BC = sqrt(2), and CA = 1.
To find the perimeter, we add the lengths of all three sides:
Perimeter = AB + BC + CA
Perimeter = 1 + sqrt(2) + 1
Simplifying the expression, we get:
Perimeter = 2 + sqrt(2)
The exact value of the perimeter is 2 + sqrt(2). However, in the given options, the closest value is 2. Therefore, the correct answer is option C: 2 2.
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The perimeter of the triangle formed by the points A(0,0), B(1,0) and C(0,1) isa)√2 + 1b)1 ± √2c)2 + √2d)3Correct answer is option 'C'. Can you explain this answer?
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