Answer:
D.√85
Step-by-step explanation:
We can find the distance between two points using the distance between two points formula
Distance between two points formula:
d = √(x2 - x1)² + (y2 - y1)²
Where the x and y values are derived from the given points
We are given the two points (-2,7) and (7,9)
Using these points let's define the variables ( variables are x1, x2, y1, and y2)
Remember points are written as follows (x,y)
The x value of the first point is -2 so x1 = -2
The x value of the second point is 7 so x2 = 7
The y value of the first point is 7 so y1 = 7
The y value of the second point is 9 so y2 = 9
Now that we have defined each variable let's find the distance between the two points
We can do this by substituting the values into the formula
Formula: d = √(x2 - x1)² + (y2 - y1)²
Variables: x1 = -2, x2 = 7, y1 = 7, y2 = 9
Substitute values in formula
d = √(7 - (-2))² + (9 - 7)²
Evaluation:
The two negative signs cancel out on 7-(-2) and it changes to +7
d = √ (7+2)² + (9-7)²
Add 7+2 and subtract 9 and 7
d = √ (9)² + (2)²
Simplify exponents 9² = 81 and 2² = 4
We then have d = √ 81 + 4
Finally we add 81 and 4
We get that the distance between the two points is √85
![\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &S&(~ -6 &,& 7~) % (c,d) &T&(~ -3 &,& 4~) \end{array}\\\\\\ % distance value d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ ST=\sqrt{[-3-(-6)]^2+[4-7]^2}\implies ST=\sqrt{(-3+6)^2+(4-7)^2} \\\\\\ ST=\sqrt{3^2+(-3)^2}\implies ST=\sqrt{18}\implies ST=\sqrt{9\cdot 2} \\\\\\ ST=\sqrt{3^2\cdot 2}\implies ST=3\sqrt{2}](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~~~~~~~%5Ctextit%7Bdistance%20between%202%20points%7D%5C%5C%5C%5C%0A%5Cbegin%7Barray%7D%7Bccccccccc%7D%0A%26%26x_1%26%26y_1%26%26x_2%26%26y_2%5C%5C%0A%25%20%20%28a%2Cb%29%0A%26S%26%28~%20-6%20%26%2C%26%207~%29%20%0A%25%20%20%28c%2Cd%29%0A%26T%26%28~%20-3%20%26%2C%26%204~%29%0A%5Cend%7Barray%7D%5C%5C%5C%5C%5C%5C%20%0A%25%20%20distance%20value%0Ad%20%3D%20%5Csqrt%7B%28%20x_2-%20x_1%29%5E2%20%2B%20%28%20y_2-%20y_1%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0AST%3D%5Csqrt%7B%5B-3-%28-6%29%5D%5E2%2B%5B4-7%5D%5E2%7D%5Cimplies%20ST%3D%5Csqrt%7B%28-3%2B6%29%5E2%2B%284-7%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0AST%3D%5Csqrt%7B3%5E2%2B%28-3%29%5E2%7D%5Cimplies%20ST%3D%5Csqrt%7B18%7D%5Cimplies%20ST%3D%5Csqrt%7B9%5Ccdot%202%7D%0A%5C%5C%5C%5C%5C%5C%0AST%3D%5Csqrt%7B3%5E2%5Ccdot%202%7D%5Cimplies%20ST%3D3%5Csqrt%7B2%7D)
