32) √58 34) 4√13 36)5√2
Explanation:
We would apply the distance formula:
√[(change in x)^2 + (change in y)^2]
32) T(4,5) and S(-3,2)
[tex]\begin{gathered} \text{distance ST = }\sqrt{(4-(-3))^2+(5-2)^2} \\ =\text{ }\sqrt{(4+3)^2+(3)^2}\text{ = }\sqrt{7^2\text{ + 9}} \\ =\text{ }\sqrt{49+9\text{ }}\text{ = }\sqrt{58} \end{gathered}[/tex]
34) Y(5,6) and X(-3, -6)
[tex]\begin{gathered} \text{distance YX = }\sqrt{(5-(-3))^2+(6-(-6))^2} \\ =\text{ }\sqrt{(5+3)^2+(6+6)^2}\text{ = }\sqrt{8^2+12^2} \\ =\sqrt{64+144} \\ =\text{ }\sqrt{208\text{ =}}\sqrt{4\times4\times13} \\ =\text{ 2}\times2\times\sqrt{13}\text{ } \\ \text{= 4}\sqrt{13} \end{gathered}[/tex]
36) X(1,4) and Y(6,9)
[tex]\begin{gathered} \text{distance XY = }\sqrt{(1-6)^2+(4-9)^2} \\ =\text{ }\sqrt{-5^2+(-5)^2}\text{ = }\sqrt{25\text{ + 25}} \\ =\text{ }\sqrt{50\text{ = }}\sqrt{(2\times25}) \\ =\text{ 5}\sqrt{2} \end{gathered}[/tex]
32) √58 34) 4√13 36)5√2
