Question

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Answer 1

Answer:

DE = m unit , Slope DE = 0 , Mid point of DE = $(\frac{m}{2},n)$

EF = n unit , Slope EF = Undefined , Mid point of EF = $(m,\frac{n}{2})$

DF = √(m²+n²) unit , Slope DF = -n / m, Mid point of DF = $(\frac{m}{2},\frac{n}{2})$

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:

$l(DE) = \sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} )}$

$l(DE) = \sqrt{(m-0)^{2}+(n-n)^{2} )}\\l(DE) = \sqrt{(m-0)^{2}+(0)^{2} )}\\l(DE) = \sqrt{(m)^{2} }\\l(DE) = m\ unit$

Similarly,

$l(EF) = \sqrt{((x_{3}-x_{2})^{2}+(y_{3}-y_{2})^{2} )}\\l(EF) = \sqrt{((m-m)^{2}+(0-n)^{2} )}\\l(EF) = \sqrt{((0)^{2}+(-n)^{2} )}\\l(EF) = \sqrt{(n)^{2}}\\l(EF) = n\ unit$

Similarly,

$l(DF) = \sqrt{((x_{3}-x_{1})^{2}+(y_{3}-y_{1})^{2} )}\\l(DF) = \sqrt{((m-0)^{2}+(0-n)^{2} )}\\l(DF) = \sqrt{((m)^{2}+(n)^{2} )}\ units$

Slope Formula:

$Slope(DE)=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\\\\Slope(DE)=\frac{n-n}{m-0}\\\\Slope(DE)=0$

Similarly,

$Slope(EF)=\frac{y_{3}-y_{2} }{x_{3}-x_{2}}\\\\Slope(EF)=\frac{0-n}{m-m}\\\\Slope(EF)=Infinity$

Similarly,

$Slope(DF)=\frac{y_{3}-y_{1} }{x_{3}-x_{1} }\\\\Slope(DE)=\frac{0-n}{m-0}\\\\Slope(DE)=\frac {-n}{m}$

Section Formula:

$Mid\ point(DE)=(\frac{x_{1}+x_{2} }{2}, \frac{y_{1}+y_{2} }{2})=(\frac{m}{2},n)$

Similarly,

$Mid\ point(EF)=(\frac{x_{3}+x_{2} }{2}, \frac{y_{3}+y_{2} }{2})=(m,\frac{n}{2})$

Similarly,

$Mid\ point(DE)=(\frac{x_{1}+x_{3} }{2}, \frac{y_{1}+y_{3} }{2})=(\frac{m}{2},\frac{n}{2})$

DE = m unit , Slope DE = 0 , Mid point of DE = $(\frac{m}{2},n)$

EF = n unit , Slope EF = Undefined , Mid point of EF = $(m,\frac{n}{2})$

DF = √(m²+n²) unit , Slope DF = -n / m, Mid point of DF = $(\frac{m}{2},\frac{n}{2})$