How do you find the possible values for a if the points (-5,a), (3,1) has a distance of #sqrt89#?
2 Answers
Explanation:
The formula for distance of two Points is given by
so we get
squaring we get
combining like Terms
using the quadratic formula we get
so
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#