Question

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

Answer 1

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).