Triangle ABC is graphed on the coordinate plane, perimeter of ΔABC is 30.
What is the distance formula?
The distance formula is the formula, which is used to find the distance between any two points, only if the coordinates are known to us. These coordinates could lie in x-axis or y-axis or both. Suppose, there are two points, say P and Q in an XY plane. The coordinates of point P are (x1,y1) and of Q are (x2,y2). Then the formula to find the distance between two points PQ is given by:
PQ = [tex]\sqrt{(x_{2}-x_{1} )^{2}+(y_{2}-y_{1} )^{2} }[/tex]
Distance formula in coordinate geometry
D = [tex]\sqrt{(x_{2}-x_{1} )^{2}+(y_{2}-y_{1} )^{2} }[/tex]
A (x1, y1) = (-6, 3) , B(x2, y2) = (-6,-2)
Distance of AB = [tex]\sqrt{(-6-(-6))^{2}+(-2-3)^{2} }[/tex]
Distance of AB = [tex]\sqrt{0+25}[/tex] = 5
A (x1, y1) = (-6, 3) , C(x2, y2) = (6,-2)
Distance of AC = [tex]\sqrt{(6-(-6))^{2}+(-2-3)^{2} }[/tex]
Distance of AC = [tex]\sqrt{144+25}[/tex] = [tex]\sqrt{169}[/tex] = 13
B (x1, y1) = (-6, -2) , C(x2, y2) = (6,-2)
Distance of BC = [tex]\sqrt{(6-(-6))^{2}+(-2-(-2))^{2} }[/tex]
Distance of BC = [tex]\sqrt{144+0}[/tex] = 12
Perimeter of ΔABC = Distance of AB + Distance of AC + Distance of BC
P = 5 + 13 +12
P = 30
Thus, Perimeter of ΔABC is 30.
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