Answer:
Distance between points A and B is, [tex]\sqrt{68}[/tex] units
Step-by-step explanation:
Given the coordinates point :
A = (4 , 2) , B = (-4, 0) and C = (4, 0)
Using distance formula:
i,e
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
First calculate the length of AC ;
where A = (4, 2) and C = (4, 0)
then using distance formula;
[tex]AC= \sqrt{4-4)^2+(0-2)^2}[/tex]
[tex]AC= \sqrt{(0)^2+(-2)^2}[/tex]
[tex]AC= \sqrt{4}[/tex] = 2 units.
Similarly, calculate the length of BC;
Using distance formula on the given points B =(-4, 0) and C = (4, 0)
then;
[tex]BC= \sqrt{4+4)^2+(0-0)^2}[/tex]
[tex]BC= \sqrt{8)^2}[/tex] = 8 units.
Now, using Pythagorean theorem in triangle ACB; to find the distance AB
[tex]AB^2=AC^2+BC^2[/tex]
Substitute the values of AC = 2 units and BC = 8 units;
[tex]AB^2 =2^2+8^2[/tex]
Simplify:
[tex]AB^2 =4+64 = 68[/tex]
or
[tex]AB= \sqrt{68}[/tex] units.
Therefore, the distance between points A and B is, [tex]\sqrt{68}[/tex] units
