What is the perimeter of a triangle with vertices of (2,0), (2, -3) and (-2,-3)?

#" "#
#"Given Vertices: "color(red)( A(2,0), B(2,-3) and C(-2,-3)#

#color(green)("Step 1:"#

Construct a triangle ABC with the given vertices:

#color(green)("Step 2:"#

Perimeter of the triangle ABC : #color(blue)(bar(AB)+bar(BC)+bar(AC)#

#bar(AB) " refers to the distance between the two points A and B"#.

To find the magnitudes of the sides AB, BC and AC, use the distance formula:

#"Distance between two points " = color(red)(sqrt((x_2-x_1)^2+(y_2-y_1)^2)#

#color(green)("Step 3:"#

Distance(D) between the two points: #color(brown)(A(2,0) and B(2,-3)#

#D = bar(AB) = sqrt((2-2)^2+(-3-0)^2)#

#rArr sqrt(9)#

#rArr 3#

#"Distance between the Points A and B: 3 Units"#

#color(green)("Step 4:"#

Distance between two points: #color(brown)(B(2,-3) and c(-2,-3)#

#D =bar(BC) = sqrt((-2-2)^2+(-3-(-3)^2)#

#rArr sqrt((-4)^2)#

#rArr sqrt(16#

#rArr 5#

#"Distance between the Points B and C: 4 Units"#

#color(green)("Step 5:"#

Distance between two points: #color(brown)(A(2,0) and C(-2,-3)#

#D = bar(AC)=sqrt((-2-2)^2+(-3-0)^2)#

#rArr sqrt((-4)^2+(-3)^2)#

#rArr sqrt(16+9#

#rArr sqrt(25)#

#rArr 5#

#"Distance between the Points A and C: 5 Units"#

#color(green)("Step 6:"#

Hence, the Perimeter of the triangle ABC

#=3+4+5=12 " Units"#

#color(green)("Step 7:"#

Measure the distances between points on the coordinate plane:

#color(green)("Step 8:"# Useful information

Measure the angle #/_ ABC#

Verify that the angle is #90^@#

Hence, triangle #ABC# is a right-triangle.

Hope it helps.

Therefore, with no work at all, you know that the perimeter is 12. #color(white)(mmmmmmm)#__