Respuesta :
The distance formula is given by:
[tex]d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }[/tex]
We are given two points A and B as
A(1,1) and
B(7,-7)
so we have ,
x1 = 1 , y1=1
x2= 7 and y2=-7
Plugging these in the formula we have:
[tex]d=\sqrt{(7-1)^{2}+(-7-1)^{2} }[/tex]
d=√(36+64)
d=√100
d=10
Answer: The distance between A(1,1) and B(7,-7) is 10
Answer:
d=10 units
Step-by-step explanation:
Hello.
Step 1
the formula of the distance between two points is based on the Pythagorean theorem, which states that in a rectangle :
[tex]side^{2} +side^{2}=hypotenuse^{2}\\[/tex]
Now, suppose we have two points P1(X1,Y1) and P2(X2,Y2), the distance between the two points will be the hypotenuse of our triangle, the difference in x will be the adjacent leg, and the difference in coordinates in y will be our opposite leg.
adjacent side =X2-X1
opposite side=Y2-Y1
hypotenuse=distance between P1 and P2
replacing
[tex]adjacent\ leg^{2} +opposite\ leg^{2}=hypotenuse^{2}\\(x_{2}-x_{1}) ^{2} +(y_{2}-y_{1})^{2}=(distance between\ P1\ and\ P2)^{2}\\ distance between\ P1\ and\ P2=\sqrt{(x_{2}-x_{1}) ^{2} +(y_{2}-y_{1})^{2}} \\\\[/tex]
we take only the positive root because it is a distance, a negative distance makes no sense
Step 2
find the distance between A(1,1) and B (7,-7) using the formula
Let
P1=A(1,1)
P2=B(7,-7)
put the values into the formula
[tex]d=\sqrt{(x_{2}-x_{1}) ^{2} +(y_{2}-y_{1})^{2}} \\let\\\\x_{1}=1,y_{1}=1,x_{2}=7,y_{2}=-7\\d=\sqrt{(7-1) ^{2} +(-7-(1))^{2}}\\d=\sqrt{(6) ^{2} +(-8)^{2}}\\d=\sqrt{36 +64}\\d=\sqrt{100}\\ d=10[/tex]
d=10 units
Have a good day.
