The distance from point A(x, 1) to point B(0, 7) is equal to 10. Calculate the value of the abscissa x.
Mathematics
Leshawna
Question
The distance from point A(x, 1) to point B(0, 7) is equal to 10. Calculate the value of the abscissa x.
2 Answer

1. User Answers RauwAle
Point distance :
After performing the calculations, we conclude that the value of the abscissa "x" is 8.
To find the answer, let's use the formula to calculate the distance between two points:
[tex] \bold{d_{AB}^2=(x_bx_a)^2+(y_by_a)}[/tex]
Substituting the values in the formula, we get:
[tex]\begin{gathered} \bold{10^2=(0x)^2+(71)^2}\\ \bold{100=x^2+7^2+2\times 7\times 1+1^2}\\ \bold{100=x^2+4913}\\ \bold{100=x^2+36}\\ \bold{x^2=10036\\x^2=64}\\ \bold{x=\sqrt{64}}\\\\ \boxed{{\boxed{ \bold{ x=8}}}}\end{gathered}[/tex]

2. User Answers mhanifa
Answer:
 The abscissa is one of x = 8 or x =  8

Use the distance formula:
 [tex]d=\sqrt{(x_2x_1)^2+(y_2y_1)^2}[/tex]
Given:
 x₁ = x, x₂ = 0, y₁ = 1 , y₂ = 7, d = 10
Substitute these values and solve for x:
 [tex]10=\sqrt{(0x)^2+(71)^2}[/tex]
 [tex]10=\sqrt{x^2+6^2}[/tex]
 [tex]10^2=x^2+36[/tex]
 [tex]100 = x^2+36[/tex]
 [tex]x^2=64[/tex]
 [tex]x=\sqrt{64}[/tex]
 [tex]x=8,\ or \ x = 8[/tex]