How do I work this geometry problem

How do you work this problem?

”use the distance formula and the pythagorean theorem to find the distance to the nearest 10th from T(4, -2) To U(-2, 3)”

I already know the answer is 7.8 because the teacher gave us the answer but I need to know how to work it! thanks

given two points (x1,y1) and (x2,y2) the distance formula is

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

d = sqrt((- 2 - 4)^2 + (3 - - 2)^2)

d = sqrt((- 6)^2 + 5^2)

d = sqrt(36 + 25)

d = sqrt(61)

d = 7.8

Hi, I think it'd be helpful to plot the points on a graph first, to give yourself an image of the problem.

After plotting the points T(4,-2) and U(-2,3), you'll want to make them two corners of a right triangle. So, dropping a line down from U, and from T, to form a right angle with those two lines. Then, you can tell the length of both of those lines, the vertical being a length of 5, and the horizontal being 6. From there, the Pythagorean theorem can be used, so sqrt(5^2+6^2)=hypotenuse, and the hypotenuse is, in this case, the distance between the two points.

Using the Pythagorean theorem in this sense, is where the distance formula d=sqrt[(x2-x1)^2+(y2-y1)^2] came about from. Since the (x2-x1) is just determining the length of the horizontal side of the triangle we drew, and similarly for the (y2-y1) part being the vertical side of the triangle.

Hope that helped!

I hate geometry. It's ruining my gpa. SCREW YOU GEOMETRY. But sorry I don't know how to do it :( I don't even know why they teach us geo. It's not like we need it to survive in the real world. Like seriously, who's gonna measure the circumference of a circle for fun?

distance=√[(4+2)²+(-2-3)²]
=√(36+25)
=√61
=7.8

You use the distance formula and the pythagorean theorem , and it's easy

Difference of y = 5
Difference of x = -6
25+36 = 61
sqrt(61) = 7.8