The length of the line segment joining A(2,-1) and B(5,y) is 5 units. What is y?

1 Answer
Jan 24, 2018

y=-5" or "y=3y=5 or y=3

Explanation:

"use the "color(blue)"distance formula"use the distance formula

color(red)(bar(ul(|color(white)(2/2)color(black)(d=sqrt((x_2-x_1)^2+(y_2-y_1)^2))color(white)(2/2)|)))

"let "(x_1,y_1)=(2,-1)" and "(x_2,y_2)=(5,y)

d=sqrt((5-2)^2+(y+1)^2)=5

rArrd=sqrt(9+(y+1)^2)=5

color(blue)"squaring both sides"

rArr9+(y+1)^2=25

rArr(y+1)^2=25-9=16

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

rArry+1=+-sqrt16larrcolor(blue)"note plus or minus"

rArry+1=+-4

rArry=-1+-4

rArry=-1-4" or "y=-1+4

rArry=-5" or "y=3