Question

Explain the distance formula. Then use it to calculate the

distance between A(1, 1) and B(7, −7).

Answer 1

Answer: The required distance between the points between A(1, 1) and B(7, −7) is 10 units.

Step-by-step explanation: We are given to explain the distance formula. Also, to calculate the distance between A(1, 1) and B(7, −7).

Distance formula : The distance between any two two points with co-ordinates (a, b) and (c, d) is given by

`D=√((c-a)^2+(d-b)^2).`

Therefore, the distance between the points A(1, 1) and B(7, −7) is given by

`D\\\\=√((7-1)^2+(-7-1)^2)\\\\=√(36+64)\\\\=√(100)\\\\=10.`

Thus, the required distance between the points between A(1, 1) and B(7, −7) is 10 units.

Answer 2

`dAB=10\ units`

Explanation:

we know that

The distance formula is derived by creating a triangle and using the Pythagorean theorem to find the length of the hypotenuse. The hypotenuse of the triangle is the distance between the two points

The formula to calculate the distance between two points is equal to

`d=\sqrt{(y2-y1)^(2)+(x2-x1)^(2)}`

we have

A(1, 1) and B(7, −7)

Let

(x1,y1)=A(1, 1)

(x2,y2)=B(7, −7)

substitute the given values in the formula

`dAB=\sqrt{(-7-1)^(2)+(7-1)^(2)}`

`dAB=\sqrt{(-8)^(2)+(6)^(2)}`

`dAB=√(64+36)`

`dAB=√(100)`

`dAB=10\ units`