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Sketch a graph of x−y=−4Find the midpoint between (−1,4) and (−4,1)

User InnaM
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1 Answer

1 vote

Solution:

Given the equation:


x-y-=-4

To sketch the graph of the above equation,

step 1: Evaluate the value of y, when x equals zero

Thus,


\begin{gathered} x-y=-4 \\ when\text{ x=0, we have} \\ 0-y=-4 \\ \Rightarrow y=4 \end{gathered}

step 2: Evaluate the value of x, when y equals zero.

Thus,


\begin{gathered} x-y=-4 \\ when\text{ y=0, we have} \\ x-0=-4 \\ \Rightarrow x=-4 \end{gathered}

step 3: Plot the obtained points in steps 1 and 2 on a graph.

Thus, the points are


\left(0,4\right?\text{ and \lparen-4,0\rparen}

The graph of the equation is as shown below:

MIdpoint: The midpoint (x,y) between two points is expressed as


\begin{gathered} \lparen x,y)=\left((x_1+x_2)/(2),(y_1+y_2)/(2)\right? \\ where \\ \lparen x_1,y_1)\text{ and \lparen x}_1,y_1)\text{ are the coordinates of the endpoints} \end{gathered}

Given the points (-1,4) and (-4,1), we have


\begin{gathered} x_1=-1 \\ y_1=4 \\ x_2=-4 \\ y_2=1 \end{gathered}

Thus, the midpoint of the points (-1,4) and (-4, 1) is evaluated as


\begin{gathered} \lparen x,y)=\left((-1+\left(-4\right))/(2),(4+1)/(2)\right? \\ =\left((-1-4)/(2),(4+1)/(2)\right? \\ =\left(-(5)/(2),(5)/(2)\right? \\ \Rightarrow\left(x,y\right)=\left(-2.5,\text{ 2.5}\right? \end{gathered}

Hence, the midpoint between (−1,4) and (−4,1) is (-2.5, 2.5).

Sketch a graph of x−y=−4Find the midpoint between (−1,4) and (−4,1)-example-1
User Alberto Malagoli
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