Mathematics

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

  • 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_b-x_a)^2+(y_b-y_a)}[/tex]

    Substituting the values in the formula, we get:

    [tex]\begin{gathered} \bold{10^2=(0-x)^2+(7-1)^2}\\ \bold{100=x^2+7^2+2\times -7\times 1+1^2}\\ \bold{100=x^2+49-13}\\ \bold{100=x^2+36}\\ \bold{x^2=100-36\\x^2=64}\\ \bold{x=\sqrt{64}}\\\\ \boxed{{\boxed{ \bold{ x=8}}}}\end{gathered}[/tex]

  • Answer:

    • The abscissa is one of  x = 8 or x = - 8

    -------------------------------------------

    Use the distance formula:

    • [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

    Given:

    • x₁ = x, x₂ = 0, y₁ = 1 , y₂ = 7, d = 10

    Substitute these values and solve for x:

    • [tex]10=\sqrt{(0-x)^2+(7-1)^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]
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