Question

The distance between two points is 13. If the two points are P(-6, x) and Q(-1, -5), which of these can be the value of x? Select all that apply.

• A.
  -18
• B.
  11
• C.
  7
• D.
  -17

Answer 1

Answer: (C), (D)

-17
We are given two points P(-6, x) and Q(-1, -5) and the distance between them is 13.

$PQ=\sqrt{(-6-(-1){)}^2+(x-(-5){)}^2}13=\sqrt{(-6+1{)}^2+(x+5{)}^2}13=\sqrt{(-5{)}^2+x^2+25+10x}13=\sqrt{25+x^2+25+10x}13=\sqrt{x^2+50+10x}\text{Squaring both sides, we get,}169=x^2+50+10x\text{squaring both sides, we get,}169=x^2+50+10x{x}^2+10x+50-169=0x^2+10x-119=0x^2+17x-7x-119=0x(x+17)-7(x+17)=0(x-7)(x+17)=0So,x=7orx=-17$

Thus, options (c) and (d) are correct.