Question

find length of three sides of triangle (-5,-1),(3,-5),(5,2)​

Answer 1

We need to recall the following to answer coordinate geometry question:

• $\text{Distance between two points } = \sqrt{ (y_{2} - y_{1} )^2 + (x_{2} - x_{1} )^2 }$

To answer this question, we need to:

• Find the length between (-5, -1) and (3, -5)
• Find the length between (3, -5) and (5, 2)
• Find the length between (5, 2) and (-5, -1)

Find the length between (-5, -1) and (3, -5):

$\text{Distance between two points } = \sqrt{ (y_{2} - y_{1} )^2 + (x_{2} - x_{1} )^2 }$

$\text{Distance} = \sqrt{ (-5 - (- 1) )^2 + (3 - (-5))^2 }$

$\text{Distance} = \sqrt{ (-4 )^2 + (8)^2 }$

$\text{Distance} = \sqrt{80}$

$\text{Distance} = 4\sqrt{5}$

$\text{Distance} = 8.94$

Find the length between (3, -5) and (5, 2):

$\text{Distance between two points } = \sqrt{ (y_{2} - y_{1} )^2 + (x_{2} - x_{1} )^2 }$

$\text{Distance} = \sqrt{ (2 - (-5) )^2 + (5 - 3)^2 }$

$\text{Distance} = \sqrt{ (7 )^2 + (2)^2 }$

$\text{Distance} = \sqrt{53}$

$\text{Distance} = 7.28$

Find the length between (-5, -1) and (5, 2):

$\text{Distance between two points } = \sqrt{ (y_{2} - y_{1} )^2 + (x_{2} - x_{1} )^2 }$

$\text{Distance} = \sqrt{ (2 - (-1) )^2 + (5 - (- 5))^2 }$

$\text{Distance} = \sqrt{ (3 )^2 + (10)^2 }$

$\text{Distance} = \sqrt{109}$

$\text{Distance} = 10.44$

Answer: The length of the three sides are 8.94 units, 7.28 units and 10.44 units.