Question

use the distance formula and the pythagorean theorem to find the distance, to the nearest tenth, from T (4,-2) to (-2,3).

Answer 1

Answer:
distance = $\sqrt{61}$ which is 7.8 to the nearest tenth

Explanation:
The distance between two points can be calculated using the following formula:
distance = $\sqrt{(x2 - x1)^2 + (y2 - y1)^2}$

In the given, we have:
point (4,-2) representing (x1,y1)
point (-2,3) representing (x2,y2)

Substitute with the givens in the above formula to get the distance as follows:
distance = $\sqrt{(-2-4)^2 + (3--2)^2} = \sqrt{61}$ which is 7.8 to the nearest tenth

Hope this helps :)

Answer 2

T=(4, -2)=(xt, yt)→xt=4, yt=-2
P=(-2, 3)=(xp, yp)→xp=-2, yp=3

d=sqrt[ (xp-xt)^2+(yp-yt)^2 ]
d=sqrt[ (-2-4)^2+(3-(-2))^2 ]
d=sqrt[ (-6)^2+(3+2)^2 ]
d=sqrt[ 36+(5)^2 ]
d=sqrt( 36+25 )
d=sqrt(61)
d=7.810249676
To the nearest tenth
d=7.8

Answer: The distance, to the nearest tenth, from T (4,-2) to (-2,3) is 7.8