Compute distance between the 2 points (1- √2, -1) & (2+√2, 4). Show work.?
回答 (6)
2018-01-01 12:49 am
✔ 最佳答案
Use the distance formula, which is based on the Pythagorean Theorem. 
2018-01-01 12:00 am
Distance between (x₁, y₁) and (x₂, y₂)
= √[(x₁ - x₂)² + (y₁ + y₂)²]
Hence, distance between the 2 points (1- √2, -1) and (2 + √2, 4)
= √{[(2 + √2) - (1 - √2)]² + [4 - (-1)]²}
= √ [(2 + √2 - 1 + √2)² + (4 + 1)²]
= √ [(1 + 2√2)² + (5)²}
= √[(1 + 4√2 + 8) + 25]
= √(34 + 4√2)
= √[(x₁ - x₂)² + (y₁ + y₂)²]
Hence, distance between the 2 points (1- √2, -1) and (2 + √2, 4)
= √{[(2 + √2) - (1 - √2)]² + [4 - (-1)]²}
= √ [(2 + √2 - 1 + √2)² + (4 + 1)²]
= √ [(1 + 2√2)² + (5)²}
= √[(1 + 4√2 + 8) + 25]
= √(34 + 4√2)
2018-01-01 12:12 am
Since this forms a right triangle, it's a Pythagorean equation problem
d² = x² + y²
x is Δx like (2+√2) - (1- √2)
= 2 +√2 -1+ √2
= 1 + 2√2
y is Δy like 4-(-1) = 5
Square them, add together, then take the root.
I get √[34 + 4√(2)]
≈6.29737
d² = x² + y²
x is Δx like (2+√2) - (1- √2)
= 2 +√2 -1+ √2
= 1 + 2√2
y is Δy like 4-(-1) = 5
Square them, add together, then take the root.
I get √[34 + 4√(2)]
≈6.29737
2017-12-31 11:58 pm
For the two points (a,b) & (c,d), a formula for the distance is √( (c-a)² + (d-b)² ).
Corresponding this to your two points, what are
a=?
b=?
c=?
d=?
Then, what are c-a = ? and d-b = ?
Do these and we can take it from there...!
Corresponding this to your two points, what are
a=?
b=?
c=?
d=?
Then, what are c-a = ? and d-b = ?
Do these and we can take it from there...!
2018-01-01 12:08 am
'' Show work please ''
d = √[ [(1 - √2) - (2 + √2)]^2 + [ (- 1) - 4]^2]
= √[ ( 1 - √2 - 2 - √2)^2 + ( - 5)^2]
= √[ (-1 - 2√2)^2 + 25]
= √[ 9 + 4√2 + 25]
= √{ 34 + 4√2]
= 6.297368835
= 6.3
d = √[ [(1 - √2) - (2 + √2)]^2 + [ (- 1) - 4]^2]
= √[ ( 1 - √2 - 2 - √2)^2 + ( - 5)^2]
= √[ (-1 - 2√2)^2 + 25]
= √[ 9 + 4√2 + 25]
= √{ 34 + 4√2]
= 6.297368835
= 6.3
2018-01-01 11:37 pm
d² = ( 2√2 + 1)² + 5²
d² = 8 + 1 + 4√2 + 25
d² = 34 + 4√2
d = [ 34 + 4√2 ]^(1/2)
d = 2^(1/2) [ 17 + 2√2 ]^(1/2)
d² = 8 + 1 + 4√2 + 25
d² = 34 + 4√2
d = [ 34 + 4√2 ]^(1/2)
d = 2^(1/2) [ 17 + 2√2 ]^(1/2)
收錄日期: 2021-04-18 18:01:22
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https://hk.answers.yahoo.com/question/index?qid=20171231154231AAOpZVI