Question

A=(-2,-7) B=(-6,4) C=(-2,7) D=(2,4) What is the perimeter?

Answer 1

`\displaystyle\bf\\AB=√(\Big(-6-(-2)\Big)^2+\Big(4-(-7)\Big)^2)\\\\AB=√(\Big(-6+2\Big)^2+\Big(4+7\Big)^2)\\\\AB=√(\Big(-4\Big)^2+\Big(11\Big)^2)\\\\AB=√(16+121)\\\\\boxed{\bf AB=√(137)}`

.

`\displaystyle\bf\\BC=√(\Big(-2-(-6)\Big)^2+\Big(7-4\Big)^2)\\\\BC=√(\Big(-2+6\Big)^2+\Big(7-4\Big)^2)\\\\BC=√(\Big(4\Big)^2+\Big(3\Big)^2)\\\\BC=√(16+9)\\\\BC=√(25)\\\\\boxed{\bf BC=5}`

.

`\displaystyle\bf\\CD=√(\Big(2-(-2)\Big)^2+\Big(4-7\Big)^2)\\\\CD=√(\Big(2+2\Big)^2+\Big(4-7\Big)^2)\\\\CD=√(\Big(4\Big)^2+\Big(-3\Big)^2)\\\\CD=√(16+9)\\\\CD=√(25)\\\\\boxed{\bf CD=5}`

.

`\displaystyle\bf\\AD=√(\Big(2-(-2)\Big)^2+\Big(4-(-7)\Big)^2)\\\\AD=√(\Big(2+2\Big)^2+\Big(4+7\Big)^2)\\\\AD=√(\Big(4\Big)^2+\Big(11\Big)^2)\\\\AD=√(16+121)\\\\\boxed{\bf AD=√(137)}`

.

`\displaystyle\bf\\P=AB+BC+CD+AD=√(137)+5+5+√(137)\\\\\boxed{\bf P=10+2√(137)}`