Question

Please help! Numbers 32, 34 and 36! Find the distanceThis is number 36: X(1,4), Y(6,9)

Answer 1

32) √58 34) 4√13 36)5√2

Step-by-step explanation:

We would apply the distance formula:

√[(change in x)^2 + (change in y)^2]

32) T(4,5) and S(-3,2)

`\begin{gathered} \text{distance ST = }√((4-(-3))^2+(5-2)^2) \\ =\text{ }√((4+3)^2+(3)^2)\text{ = }\sqrt{7^2\text{ + 9}} \\ =\text{ }\sqrt{49+9\text{ }}\text{ = }√(58) \end{gathered}`

34) Y(5,6) and X(-3, -6)

`\begin{gathered} \text{distance YX = }√((5-(-3))^2+(6-(-6))^2) \\ =\text{ }√((5+3)^2+(6+6)^2)\text{ = }√(8^2+12^2) \\ =√(64+144) \\ =\text{ }\sqrt{208\text{ =}}√(4*4*13) \\ =\text{ 2}*2*√(13)\text{ } \\ \text{= 4}√(13) \end{gathered}`

36) X(1,4) and Y(6,9)

`\begin{gathered} \text{distance XY = }√((1-6)^2+(4-9)^2) \\ =\text{ }√(-5^2+(-5)^2)\text{ = }\sqrt{25\text{ + 25}} \\ =\text{ }\sqrt{50\text{ = }}√((2*25)) \\ =\text{ 5}√(2) \end{gathered}`

32) √58 34) 4√13 36)5√2