The length of the line segment joining A(2,8) and B(12,y) is 26 units. What is y?
2 Answers
Explanation:
Distance between two points is calculated using the formula,
Given : x1 = 2, x2 = 12, y1 = 8, y2 = y & d = 26 units
Squaring both sides,
Taking square root on both sides,
Explanation:
#"using the "color(blue)"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)=(2,8)" and "(x_2,y_2)=(12,y)#
#d=sqrt((12-2)^2+(y-8)^2)=26#
#rArrd=sqrt(100+(y-8)^2)=26#
#color(blue)"square both sides"#
#rArr100+(y-8)^2=26^2=676#
#rArr(y-8)^2=676-100=576#
#color(blue)"take the square root of both sides"#
#rArry-8=+-24larrcolor(blue)"note plus or minus"#
#rArry=8+-24#
#rArry=8-24=-16" or "y=8+24=32#