Question

Find the distance between the points (9, 8) and (5, 3).

Answer 1

Answer:

$\sqrt{41}$ units

Step-by-step explanation:

To find the distance between two points, we can use the Pythagorean theorem by creating a right-angled triangle where sides a and b are the distances between the y-coordinates and x-coordinates of each point.

First let's find the distance between the x-coordinates:

(9,8): x-coordinate is 9, and (5,3): x-coordinate is 5.

9 - 5 = 4

The first side of our triangle is 4 units.

y-coordinates:

8 - 3 = 5

The second side of our triangle is 5 units.

$a^{2} +b^{2} =c^{2}$

$4^{2} +5^{2} =c^{2} \\16 +25 =c^{2} \\41 = c^{2} \\\sqrt{41} =\sqrt{c^{2} } \\\sqrt{41} = c$

Squareroot 41 is fully simplified as 41 is a prime number.

I have attached a picture to help visualize the triangle.

Hope this helped!