Question

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

Answer 1

d=10 units

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=√(36 +64)\\d=√(100)\\ d=10`

d=10 units

Have a good day.

Answer 2

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