Question

One of the sides of a pentagon has length 12. Which of the following points, when paired with (2,3), will make a side equal to this length

(14, 15)
(2, −9)
(−2, −3)
(−9, 2)

Answer 1

(2, −9)

Explanation:

Answer 2

Given 2 points A(a,b) and M(k,l), the distance between them is found by the formula:


`|AM|= \sqrt{ (a-k)^(2) + (b-l)^(2) }`

Let (k, l)=(2, 3), substituting in the above formula:


`12= \sqrt{ (a-2)^(2) + (b-3)^(2) }`


`(a-2)^(2) + (b-3)^(2)=12 ^(2)=144`

check each of the pairs given:

for (a, b)=(14, 15):


`(a-2)^(2) + (b-3)^(2)=(14-2)^(2) + (15-3)^(2)=(12)^(2) + (12)^(2)=288`

for (a, b)=(2, -9):


`(2-2)^(2) + (-9-3)^(2)=0+(-12)^(2)=144`

for (a, b)=(-2, -3):


`(-2-2)^(2) + (-3-3)^(2)=(-4)^(2) + (-9)^(2)=16+81=97`

for (a, b)=(-9, 2):


`(-9-2)^(2) + (2-3)^(2)=(-11)^(2) + (-1)^(2)=121+1=122`



Answer: (2, -9)