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=(((x_1+x_2))/(2),((y_1+y_2))/(2))`

Then the midpoint will have the coordinates:

`M=(((9+(-4)))/(2),((2+3))/(2))=((5)/(2),(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=((y_2-y_1))/((x_2-x_1))`

Then the slope will be:

P1 ( - 2 , - 9 )

P2 ( 1 , 6 )

`m=((6-(-9)))/((1-(-2)))=(6+9)/(1+2)=(15)/(3)=5`The slope is m=5