Answer:
[tex]\sqrt{41}[/tex] 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.
[tex]a^{2} +b^{2} =c^{2}[/tex]
[tex]4^{2} +5^{2} =c^{2} \\16 +25 =c^{2} \\41 = c^{2} \\\sqrt{41} =\sqrt{c^{2} } \\\sqrt{41} = c[/tex]
Squareroot 41 is fully simplified as 41 is a prime number.
I have attached a picture to help visualize the triangle.
Hope this helped!
