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

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)