SOLVE STEP BY STEP IN DIGITAL FORMAT 4. One of the ends of a line segment of length equal to 4 is the point A (4, 1); if the ordinate of the other extreme is (-2), find its abscissa (two solutions). 5. One of the ends of a line segment of length equal to √18 is the point A (-6, 2); if the ordinate of the other end is (-1), Find its abscissa (two solutions).

4. Given :- One of the ends of a line segment of length equal to 4 is the point A(4,1); if the ordinate of the other extreme is (-2), find its abscissa.

solution :-

let abscissa of other extreme is x, then coordinate is (x,-2).

length=4

4=$\sqrt{{(x-4)}^2+{(-2-1)}^2}$

4=$\sqrt{{(x-4)}^2+{(-3)}^2}$

4=$\sqrt{x^2+16-8x+9}$

4²= x²+25-8x

x²-8x+25-16=0

x²-8x+9=0

x= $\frac{-(-8)\pm \sqrt{{(-8)}^2-4\left(1\right)\left(9\right)}}{2\left(1\right)}$

x=$\frac{8\pm \sqrt{64-36}}{2}$

x=$\frac{8\pm \sqrt{28}}{2}$

x=$4\pm \sqrt{7}$=4+$\sqrt{7}$,4-$\sqrt{7}$=6.65,1.35

hence, abscissa 6.65 or 1.35