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neonofarm [45]
4 years ago
13

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

Mathematics
2 answers:
crimeas [40]4 years ago
4 0

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

Solnce55 [7]4 years ago
4 0

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.

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What do you want to calculate?

CALCULATE IT!
Solve
Graph
Lesson

Problem:
Solve
x
+
2
y
=
−
6
;
3
x
+
8
y
=
−
20
Steps:
I will solve your system by substitution.
(You can also solve this system by elimination.)
x
+
2
y
=
−
6
;
3
x
+
8
y
=
−
20
Step: Solve
x
+
2
y
=
−
6
for x:
x
+
2
y
+
−
2
y
=
−
6
+
−
2
y
(Add -2y to both sides)
x
=
−
2
y
−
6
Step: Substitute
−
2
y
−
6
for
x
in
3
x
+
8
y
=
−
20
:
3
x
+
8
y
=
−
20
3
(
−
2
y
−
6
)
+
8
y
=
−
20
2
y
−
18
=
−
20
(Simplify both sides of the equation)
2
y
−
18
+
18
=
−
20
+
18
(Add 18 to both sides)
2
y
=
−
2
2
y
2
=
−
2
2
(Divide both sides by 2)
y
=
−
1
Step: Substitute
−
1
for
y
in
x
=
−
2
y
−
6
:
x
=
−
2
y
−
6
x
=
(
−
2
)
(
−
1
)
−
6
x
=
−
4
(Simplify both sides of the equation)
Answer:
x
=
−
4
and
y
=
−
1
3 0
4 years ago
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