Answer:
DE = m unit , Slope DE = 0 , Mid point of DE = [tex](\frac{m}{2},n)[/tex]
EF = n unit , Slope EF = Undefined , Mid point of EF = [tex](m,\frac{n}{2})[/tex]
DF = √(m²+n²) unit , Slope DF = -n / m, Mid point of DF = [tex](\frac{m}{2},\frac{n}{2})[/tex]
Step-by-step explanation:
Given:
point D( x₁ , y₁) ≡ ( 0 ,n)
point E( x₂ , y₂) ≡ (m , n)
point F( x₃ , y₃) ≡ ( m ,0)
To Find:
DE = ? , Slope DE = ? , Mid point of DE = ?
EF = ? , Slope EF = ? , Mid point of EF = ?
DF = ? , Slope DF = ? , Mid point of DF = ?
Solution:
We will use Distance Formula,Slope Formula, and Section Formula.
Distance Formula:
[tex]l(DE) = \sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} )}[/tex]
[tex]l(DE) = \sqrt{(m-0)^{2}+(n-n)^{2} )}\\l(DE) = \sqrt{(m-0)^{2}+(0)^{2} )}\\l(DE) = \sqrt{(m)^{2} }\\l(DE) = m\ unit[/tex]
Similarly,
[tex]l(EF) = \sqrt{((x_{3}-x_{2})^{2}+(y_{3}-y_{2})^{2} )}\\l(EF) = \sqrt{((m-m)^{2}+(0-n)^{2} )}\\l(EF) = \sqrt{((0)^{2}+(-n)^{2} )}\\l(EF) = \sqrt{(n)^{2}}\\l(EF) = n\ unit[/tex]
Similarly,
[tex]l(DF) = \sqrt{((x_{3}-x_{1})^{2}+(y_{3}-y_{1})^{2} )}\\l(DF) = \sqrt{((m-0)^{2}+(0-n)^{2} )}\\l(DF) = \sqrt{((m)^{2}+(n)^{2} )}\ units[/tex]
Slope Formula:
[tex]Slope(DE)=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\\\\Slope(DE)=\frac{n-n}{m-0}\\\\Slope(DE)=0[/tex]
Similarly,
[tex]Slope(EF)=\frac{y_{3}-y_{2} }{x_{3}-x_{2}}\\\\Slope(EF)=\frac{0-n}{m-m}\\\\Slope(EF)=Infinity[/tex]
Similarly,
[tex]Slope(DF)=\frac{y_{3}-y_{1} }{x_{3}-x_{1} }\\\\Slope(DE)=\frac{0-n}{m-0}\\\\Slope(DE)=\frac {-n}{m}[/tex]
Section Formula:
[tex]Mid\ point(DE)=(\frac{x_{1}+x_{2} }{2}, \frac{y_{1}+y_{2} }{2})=(\frac{m}{2},n)[/tex]
Similarly,
[tex]Mid\ point(EF)=(\frac{x_{3}+x_{2} }{2}, \frac{y_{3}+y_{2} }{2})=(m,\frac{n}{2})[/tex]
Similarly,
[tex]Mid\ point(DE)=(\frac{x_{1}+x_{3} }{2}, \frac{y_{1}+y_{3} }{2})=(\frac{m}{2},\frac{n}{2})[/tex]
DE = m unit , Slope DE = 0 , Mid point of DE = [tex](\frac{m}{2},n)[/tex]
EF = n unit , Slope EF = Undefined , Mid point of EF = [tex](m,\frac{n}{2})[/tex]
DF = √(m²+n²) unit , Slope DF = -n / m, Mid point of DF = [tex](\frac{m}{2},\frac{n}{2})[/tex]
