Question

a)For(9,2)and(-4,3),findthedistancebetweenthetwopointsandthecoordinatesofthemidpointofthetwopoints.b)For(-2,-9)and(1,6),findtheslopeofthelinethroughthepairofpoints.

Answer 1

a) The distance between two points is determined following the next formula:

$d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}$

You have the points:

P1 ( 9 , 2 ) X1=9 Y1=2

P2 ( - 4 , 3 ) X2=-4 Y2=3

Then the distance is:

$d=\sqrt[]{(-4-9)^2+(3-2)^2}$$d=\sqrt[]{(-13)^2+1^2}$$d=\sqrt[]{169+1}=\sqrt[]{170}=13.03$The distance between the two points is 13.03 units.

The coordinate of the midpoint is calculated following the next formula:

$M=(\frac{(x_1+x_2)}{2},\frac{(y_1+y_2)}{2})$

Then the midpoint will have the coordinates:

$M=(\frac{(9+(-4))}{2},\frac{(2+3)}{2})=(\frac{5}{2},\frac{5}{2})$The midpoint is M= (5/2 , 5/2)

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b) the slope(m) can be found using two points with the next formula:

$m=\frac{(y_2-y_1)}{(x_2-x_1)}$

Then the slope will be:

P1 ( - 2 , - 9 )

P2 ( 1 , 6 )

$m=\frac{(6-(-9))}{(1-(-2))}=\frac{6+9}{1+2}=\frac{15}{3}=5$The slope is m=5