Given (11,2) and (x,−4), find all x such that the distance between these two points is 10. Separate multiple answers with a comma.

Question

Given (11,2) and (x,−4), find all x such that the distance between these two points is 10. Separate multiple answers with a comma.

in progress 0
Ladonna 4 years 2021-08-21T04:31:50+00:00 1 Answers 7 views 0

Answers ( )

  1. danthu
    0
    2021-08-21T04:33:47+00:00
    Reply

    Answer: x = 3, 19

    Step-by-step explanation:

    Given

    Two points i.e.  (11,2)\ \text{and}\ (x,-4) are given

    Distance between them is 10 units

    Distance is given by the distance formula

    \Rightarrow d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

    Distance between two points is

    \Rightarrow 10=\sqrt{(x-11)^2+(-4-2)^2}

    Squaring both sides

    \Rightarrow 100=(x-11)^2+(-6)^2\\\Rightarrow 100=x^2+121-22x+36\\\Rightarrow x^2-22x+57=0\\\Rightarrow x^2-19x-3x+57=0\\\Rightarrow x(x-19)-3(x-19)=0\\\Rightarrow (x-19)(x-3)=0

    i.e. x\ \text{can be }\ x=3\ or\ 19

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )