Question

Explain the distance formula. Then use it to calculate the distance between A(1,1) and B (7,-7)

Answer 1

The distance formula is given by:

$d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} }$

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:

$d=\sqrt{(7-1)^{2}+(-7-1)^{2} }$

d=√(36+64)

d=√100

d=10

Answer: The distance between A(1,1) and B(7,-7) is 10

Answer 2

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 :

$side^{2} +side^{2}=hypotenuse^{2}$

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

$adjacent\ leg^{2} +opposite\ leg^{2}=hypotenuse^{2}\\(x_{2}-x_{1}) ^{2} +(y_{2}-y_{1})^{2}=(distance between\ P1\ and\ P2)^{2}\\ distance between\ P1\ and\ P2=\sqrt{(x_{2}-x_{1}) ^{2} +(y_{2}-y_{1})^{2}}$

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

$d=\sqrt{(x_{2}-x_{1}) ^{2} +(y_{2}-y_{1})^{2}} \\let\\\\x_{1}=1,y_{1}=1,x_{2}=7,y_{2}=-7\\d=\sqrt{(7-1) ^{2} +(-7-(1))^{2}}\\d=\sqrt{(6) ^{2} +(-8)^{2}}\\d=\sqrt{36 +64}\\d=\sqrt{100}\\ d=10$

d=10 units

Have a good day.