Question

1- For the points (-2,7) and (-4,5),(a) Find the exact distance between the points.(b) Find the midpoint of the line segment whose endpoints are the given points.----------------------------------------------------------------------------------------------------------------------------------2- Graph the equation y= -3x+2 on the viewing window defined by [-10,10,1} by [-10,10,1].---------------------------------------------------------------------------------------------------------------------------3-The endpoints of a diameter of a circle are (-7,2) and(-13,10) .(a) Write an equation of the circle in standard form.(b) Graph the circle.---------------------------------------------------------------------------------------------------------------------------4- Refer to the function . f= {(6,10), (-5,8), (4,6), (2,7)}For what value of X for which f(x)=10 is {.......} ?-------------------------------------------------------------------------------------------------------------------------5-Write the domain in interval notation.(a) w(x)= lx+1l+4(b) y(x)= X ➗ lx+1l+4(c) Z(x)= X ➗ lx+1l-4----------------------------------------------------------------------------------------------------------------------------6- Graph the equation and identify the x- and y-intercepts.3x=2y

Answer 1

1.

(a) square root of 8

`√(8)`

(b) midpoint: (-3,8)

Step-by-step explanation:

Data:

Point 1 : (-2,7)

Point 2: (-4,5)

Formula:

. Distance

`D=√((x_2-x_1)^2+(y_2-y_1)^2)`

. Midpoint

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

Solution:

(a)

`\begin{gathered} D=√((-4-(-2))^2+(5-7)^2) \\ D=√((-2)^2+(-2)^2) \\ D=√(4+4) \\ D=√(8) \end{gathered}`

(b)

`\begin{gathered} M_(pt)=((-4+(-2))/(2),(5+7)/(2)) \\ M_(pt)=((-6)/(2),(12)/(2)) \\ M_(pt)=(-3,6) \end{gathered}`