Question

Find the perimeter of △ABC with vertices A(−5, −5), B(3, −5), and C(−5, 1).

Answer 1

Answer:

Perimeter: 24 u

Step-by-step explanation:

In order to find the perimeter of the triangle you have to find the distance between the vertices using the distance formula and add all the distances:

Distance AB

$d=\sqrt{ ( x_{2} - x_{1} )^{2} + ( y_{2} - y_{1} )^{2} } \\d=\sqrt{ ( 3 - (-5) )^{2} + ( (-5) - (-5) )^{2} } \\d=\sqrt{ ( 3+5 )^{2} + ( -5+5 )^{2} } \\d=\sqrt{ (8)^{2} + ( 0 )^{2} } \\d=\sqrt{ 64 } \\d=8$

Distance BC

$d=\sqrt{ ( x_{2} - x_{1} )^{2} + ( y_{2} - y_{1} )^{2} } \\d=\sqrt{ ( -5 - 3 )^{2} + ( 1 - (-5) )^{2} } \\d=\sqrt{ ( -8 )^{2} + ( 1+5 )^{2} } \\d=\sqrt{ (-8)^{2} + ( 6 )^{2} } \\d=\sqrt{64+36} \\d=\sqrt{100}\\d=10$

Distance CA

$d=\sqrt{ ( x_{2} - x_{1} )^{2} + ( y_{2} - y_{1} )^{2} } \\d=\sqrt{ ( -5 - (-5) )^{2} + ( 1 - (-5) )^{2} } \\d=\sqrt{ ( -5+5 )^{2} + ( 1+5 )^{2} } \\d=\sqrt{ (0)^{2} + ( 6 )^{2} } \\d=\sqrt{36} \\d=6$

Adding all the 3 distances we have that:

P=8+10+6=24 u