How do you find the possible values for a if the points (-5,a), (3,1) has a distance of sqrt89?

2 Answers
Sonnhard
Jun 24, 2018

a=6 or a=-4

Explanation:

The formula for distance of two Points is given by

d(P_1,P_2)=sqrt((x_2-x_1)^2+(y_2-y_1)^2)
so we get

sqrt((-5-3)^2+(a-1)^2)=sqrt(89)

squaring we get

64+a^2-2a+1=89
combining like Terms

a^2-2a-24=0

using the quadratic formula we get

a_(1,2)=1+pmsqrt(25)

so
a_1=6
a_2=-4

Jim G.
Jun 24, 2018

a=-4" or "a=6

Explanation:

"to calculate the distance d use the "color(blue)"distance formula"

•color(white)(x)d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)

"let "(x_1,y_1)=(3,1)" and "(x_2,y_2)=(-5,a)

d=sqrt((-5-3)^2+(a-1)^2)=sqrt89

sqrt(64+(a-1)^2)=sqrt89

color(blue)"square both sides"

64+(a-1)^2=89

"subtract 64 from both sides"

(a-1)^2=25

color(blue)"take the square root of both sides"

sqrt((a-1)^2)=+-sqrt25larrcolor(blue)"note plus or minus"

a-1=+-5

"add 1 to both sides"

a=1+-5

a=1-5=-4" or "a=1+5=6

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