Question

What is the approximate distance between points A and B?

Answer 1

For this problem we will use the Pythagorean Theorem. 

a^2 + b^2 = c^2

Since we are trying to find C, or the hypotenuse.  The hypotenuse is the longest side of the triangle.

What triangle?

Starting at Point A draw a line all the way down to -4.

At Point B draw a line all the way to the right to 4.

Here you have your right triangle. 

Side A, the side opposite from Angle A is 6 units.

Side B, the side opposite from Angle B is 7 units.

Now we will plug this into the Pythagorean Theorem.

6^2 + 7^2= c^2

36+49= 85 

The square root of 85 is approximately 9.2 units. 

Answer 2

The distance between the two coordinates $A{\text{ and }}B$ is approximately $\boxed{{\mathbf{9}}{\mathbf{.2 units}}}$.

Further explanation:  

The distance between two coordinates can be found by the distance formula as,

$d = \sqrt {{{\left( {{y_2} - {y_1}} \right)}^2} + {{\left( {{x_2} - {x_1}} \right)}^2}}$  

Here, $\left( {{x_1},{y_1}} \right){\text{ and }}\left( {{x_2},{y_2}} \right)$ are the coordinates ofpoints $A{\text{ and }}B$ in the number line.

The distance cannot be negative and it is the scalar quantity

Step by step explanation:

Step 1:

First we determine the coordinates of the end points $A{\text{ and }}B$ of the given line.

It can be observed from the given line that the coordinates of end point $A{\text{ and }}B$ are $\left( {4,3} \right){\text{ and }}\left( { - 2, - 4} \right)$ respectively.

Step 2:

Now, use the distance formula to obtain the distance between the two points $A{\text{ and }}B$.

The two points are $\left( {4,3} \right){\text{ and }}\left( { - 2, - 4} \right)$.Here,${x_1} = 4$ ,${x_2} =  - 2$, ${y_1} = 3$ and ${y_2} =  - 4$.

Substitute 4 for $x_1$, $-2$ for $x_2$, 3 for $y_1$ and $-4$ for $y_2$ in the distance formula to obtain the distance as,

$\begin{aligned}d&= \sqrt {{{\left( { - 4 - \left( 3 \right)} \right)}^2} + {{\left( {\left( { - 2} \right) - \left( 4 \right)}\right)}^2}} \hfill \\d&= \sqrt {{7^2} + {6^2}} \hfill\\d&= \sqrt {49 + 36}  \hfill\\d &= \sqrt {85}\approx 9.2{\text{ units}} \hfill\\\end{aligned}$  

Therefore, the distance is approximately $9.2{\text{ units}}$.

Thus,the distance between the two coordinates $A{\text{ and }}B$ is approximately $\boxed{{\mathbf{9}}{\mathbf{.2 units}}}$.

Learn more:  

1. Learn more about distance between two points on the number line https://brainly.com/question/6278187
2. Learn more about the symmetry for a function https://brainly.com/question/1286775
3. Learn more about midpoint of the segment https://brainly.com/question/3269852

Answer details:

Grade: Middle school

Subject: Mathematics

Chapter: Straight line

Keywords: Integers, distance, point, number line, units, measurement, origin, negative numbers, positive numbers, right side, left side, difference, coordinates, straight line.