Question

practice: find the possible values for the missing coordinate given: d = √2
$d=sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$
(2,y) & (3,4)
$(x_1,y_1)$ $(x_2,y_2)$

Explanation:

Step1: Substitute values into distance formula

Given $(x_1,y_1)=(2,y)$, $(x_2,y_2)=(3,4)$ and $d = \sqrt{2}$, we substitute into $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. So $\sqrt{2}=\sqrt{(3 - 2)^2+(4 - y)^2}$.

Step2: Square both sides

Squaring both sides to get rid of the square - roots, we have $2=(3 - 2)^2+(4 - y)^2$. Since $3 - 2 = 1$, then $2=1+(4 - y)^2$.

Step3: Isolate the squared term

Subtract 1 from both sides: $(4 - y)^2=2 - 1=1$.

Step4: Take square root of both sides

Taking the square root of both sides gives $4 - y=\pm1$.

Step5: Solve for y when $4 - y = 1$

Subtract 4 from both sides: $-y=1 - 4=-3$, so $y = 3$.

Step6: Solve for y when $4 - y=-1$

Subtract 4 from both sides: $-y=-1 - 4=-5$, so $y = 5$.

Answer:

$y = 3$ or $y = 5$