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The graph is a straight line that passes through the points P and Q How can I state the coordinates of P and Q. How can i determine the gradient of the line segment PQ? How do I do a equation of the line PQ ? How can I find the length of Line PQ? How can I find the mid point of PQ?

The Graph Is A Straight Line That Passes Through The Points P And Q How Can I State The Coordinates Of P And Q How Can I Determine The Gradient Of The Line Segm class=

Sagot :

Solution:

Given the graph:

(a) The coordinates of P(x,y) and Q(x,y) are;

[tex]P(0,3)\text{ and }Q(-2,0)[/tex]

(b) The gradient, m of the line segment is;

[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ \text{ Where }x_1=0,y_1=3,x_2=-2,y_2=0 \end{gathered}[/tex]

Thus;

[tex]\begin{gathered} m=\frac{0-3}{-2-0} \\ \\ m=\frac{3}{2} \end{gathered}[/tex]

(c) The equation of the line is;

[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \\ \text{ Where }x_1=0,y_1=3,m=\frac{3}{2} \end{gathered}[/tex]

Thus;

[tex]\begin{gathered} y-3=\frac{3}{2}(x-0) \\ \\ y=\frac{3}{2}x+3 \end{gathered}[/tex]

(d) The length of the line segment PQ is;

[tex]\begin{gathered} PQ=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\ \\ \text{ Where }x_1=0,y_1=3,x_2=-2,y_2=0 \end{gathered}[/tex]

Thus;

[tex]\begin{gathered} PQ=\sqrt{(-2-0)^2+(0-3)^2} \\ \\ PQ=\sqrt{13} \end{gathered}[/tex]

(e) The midpoint, MP of the line segment is;

[tex]\begin{gathered} MP=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ \\ \text{ Where }x_1=0,y_1=3,x_2=-2,y_2=0 \end{gathered}[/tex]

Thus;

[tex]\begin{gathered} MP=(\frac{0+(-2)}{2},\frac{3+0}{2}) \\ \\ MP=(-1,\frac{3}{2}) \end{gathered}[/tex]

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