Question

For each of the following pairs of points, find the length of ABa. A(0,2), B(0,1)b. A(0,10), B(24,0)C. A(5,25), B( 16,-

Answer 1

The rule of the distance between the two points (x1, y1) and (x2, y2) is

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

a.

A = (0, 2) and B = (0, 1)

Substitute (x1, y1) by (0, 2) and (x2, y2) by (0, 1) in the given rule above

$\begin{gathered} AB=\sqrt{(0-0)^2+(1-2)^2} \\ AB=\sqrt{0+1} \\ AB=\sqrt{1} \\ AB=1 \end{gathered}$

The length of AB is 1

b.

A = (0, 10) and B = (24, 0)

Substitute (x1, y1) by (0, 10) and (x2, y2) by (24, 0)

$\begin{gathered} AB=\sqrt{(24-0)^2+(0-10)^2} \\ AB=\sqrt{576+100} \\ AB=\sqrt{676} \\ AB=26 \end{gathered}$

The length of AB is 26

c.

A = (5, 25) and B = (-16, -1)

Substitute (x1, y1) by (5, 25) and (x2, y2) by (-16, -1)

$\begin{gathered} AB=\sqrt{(-16-5)^2+(-1-25)^2} \\ AB=\sqrt{(-21)^2+(-26)^2} \\ AB=\sqrt{441+676} \\ AB=\sqrt{1117} \end{gathered}$

The length of AB is square root 1117