Question

What is the distance between A(7,4) and B(-3,9) give your answer in simplest radical form

Answer 1

The distance between the given points is 5√5 (or) 11.2 units.

Explanation:

• The given points are A=(7,4) and B=(-3,9).
• You are asked to find the distance between these two points A and B.

The distance between the points represents the length of the line joining those two points.

To find the distance between any points, the distance formula is used.

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

Here, the point A (7,4) is (x1,y1) and the point B (-3,9) is (x2,y2).

Therefore, substitute x2 = -3, x1 = 7, y2 = 9 and y1 = 4 in the distance formula.

Distance =
`\sqrt{(-3-7)^(2)+(9-4)^(2) }`

⇒
`\sqrt{(-10)^(2)+(5)^(2) }`

⇒
`√(100 + 25)`

⇒
`√(125)`

⇒
`5√(5)`

The value of √5 is 2.24

⇒ 5 × 2.24

⇒ 11.2 units.

The distance between the given points is 5√5 (or) 11.2 units.