Question

Please help me by filling in the blanks! ASAP!!!

Answer 1

DE = m unit , Slope DE = 0 , Mid point of DE =
`((m)/(2),n)`

EF = n unit , Slope EF = Undefined , Mid point of EF =
`(m,(n)/(2))`

DF = √(m²+n²) unit , Slope DF = -n / m, Mid point of DF =
`((m)/(2),(n)/(2))`

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)=(y_(2)-y_(1) )/(x_(2)-x_(1) )\\\\Slope(DE)=(n-n)/(m-0)\\\\Slope(DE)=0`

Similarly,

`Slope(EF)=(y_(3)-y_(2) )/(x_(3)-x_(2))\\\\Slope(EF)=(0-n)/(m-m)\\\\Slope(EF)=Infinity`

Similarly,

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

Section Formula:

`Mid\ point(DE)=((x_(1)+x_(2) )/(2), (y_(1)+y_(2) )/(2))=((m)/(2),n)`

Similarly,

`Mid\ point(EF)=((x_(3)+x_(2) )/(2), (y_(3)+y_(2) )/(2))=(m,(n)/(2))`

Similarly,

`Mid\ point(DE)=((x_(1)+x_(3) )/(2), (y_(1)+y_(3) )/(2))=((m)/(2),(n)/(2))`

DE = m unit , Slope DE = 0 , Mid point of DE =
`((m)/(2),n)`

EF = n unit , Slope EF = Undefined , Mid point of EF =
`(m,(n)/(2))`

DF = √(m²+n²) unit , Slope DF = -n / m, Mid point of DF =
`((m)/(2),(n)/(2))`