To find the lengths of the sides of triangle ABC, we can use the distance formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
1. Length of side AB:
AB = sqrt((1 - 4)^2 + (2 - 5)^2)
= sqrt((-3)^2 + (-3)^2)
= sqrt(9 + 9)
= sqrt(18)
Therefore, the length of side AB is sqrt(18).
2. Length of side BC:
BC = sqrt((6 - 1)^2 + (2 - 2)^2)
= sqrt((5)^2 + (0)^2)
= sqrt(25 + 0)
= sqrt(25)
Therefore, the length of side BC is 5.
3. Length of side AC:
AC = sqrt((6 - 4)^2 + (2 - 5)^2)
= sqrt((2)^2 + (-3)^2)
= sqrt(4 + 9)
= sqrt(13)
Therefore, the length of side AC is sqrt(13).
4. Perimeter of triangle ABC:
Perimeter = AB + BC + AC
Perimeter = sqrt(18) + 5 + sqrt(13)
5. Area of triangle ABC:
To find the area of the triangle, we can use the Shoelace Formula or the determinant method.
For simplicity, let's use the Shoelace Formula:
Area = |(1/2)(x1y2 + x2y3 + x3y1 - x2y1 - x3y2 - x1y3)|
Area = |(1/2)((4*2) + (1*2) + (6*5) - (1*5) - (6*2) - (4*2))|
Area = |(1/2)(8 + 2 + 30 - 5 - 12 - 8)|
Area = |(1/2)(25)|
Area = 25/2
Therefore, the area of triangle ABC is 25/2.
All answers are in simplest radical form if necessary.
FIND THE MISSING SIDE LENGHTS,PERIMETER, AND AREA OF TRIANGLE ABC ON THE COORDINATE PLANE.ALL ANSWERS SHOULD BE IN SIMPLEST RADICAL FORM, IF NECESSARY. A=(4,5) B=(1,2) C=(6,2) SIDE LENGHT AB IS? SIDE LENGHT BC IS? SIDE LENGHT AC IS? PERIMETER OF TRIANGLE ABC IS? AREA OF TRIANGLE ABC IS? ANSWER CHOICES ARE- SQRT 18, SQRT 13, SQRT 5, 5, 5+3SQRT2+SQRT13, 15SQRT26, 7.5 IF YOU CAN HELP THANK YOU.
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