Question

What’s the distance between (4,-9) and (5,3)

Answer 1

`\boxed {\boxed {\sf \sqrt {145} \ or \ 12.04}}`

Explanation:

The distance between 2 points is calculated using the following formula.

`d= \sqrt {(x_2-x_1)^2+(y_2-y_1)^2)`

In this formula, (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

We know the two points are (4, -9) and (5,3). If we match the values of the points and the coordinating variable, we see that:

• x₁ = 4
• y₁= -9
• x₂ = 5
• y₂ = 3

Substitute the values into the formula.

`d= \sqrt { ( 5 -4)^2 + ( 3 --9)^2`

Solve inside the parentheses.

• (5-4)= 1
• (3 --9) = (3+9) = 12

`d= \sqrt {(1)^2 + (12)^2}`

Solve the exponents.

• (1)² = 1 *1 = 1
• (12)² = 12 * 12 = 144

`d= √( 1+144)`

Add.

`d= \sqrt{145`

Take the square root.

`d=12.04159458`

Let's round to the nearest hundredth. The 1 in the thousandth place tells us to leave the 4 in the hundredth place.

`d \approx 12.04`

The distance between the 2 points is √145 or approximately 12.04.

Answer 2

Answer: Distance = √145

Concept:

Here, we need to know the concept of the distance formula.

The distance formula is the formula, which is used to find the distance between any two points.

If you are still confused, please refer to the attachment below for a clear version of the formula.

Solve:

Given information

(x₁, y₁) = (4, -9)

(x₂, y₂) = (5, 3)

Given formula

`Distance = √((x_2-x_1)^2+(y_2-y_1)^2)`

Substitute values into the formula

`Distance = √((5-4)^2+(3+9)^2)`

Simplify values in the parentheses

`Distance = √((1)^2+(12)^2)`

Simplify exponents

`Distance = √(1+144)`

Simplify by addition

`Distance = √(145)`

Hope this helps!! :)

Please let me know if you have any questions