Answer:
The Area of Δ TOP is 43.55 units².
Step-by-step explanation:
Given:
P ≡ ( x₁ ,y₁ ) ≡ ( -5 , -7)
T ≡ ( x₂ ,y₂ ) ≡ ( 1 , 8)
O ≡ ( x₃ ,y₃ ) ≡ ( 6 , 6)
To Find :
Area of Δ TOP = ?
Solution :
We have
[tex]\textrm{Area of Triangle TOP} = \frac{1}{2}\times Base\times Height\\\textrm{Area of Triangle TOP} = \frac{1}{2}\times OT\times PT[/tex]
Now Distance formula we have
[tex]l(PT) = \sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} )}[/tex]
[tex]l(OT) = \sqrt{((x_{3}-x_{2})^{2}+(y_{3}-y_{2})^{2} )}[/tex]
Substituting the given values we get
[tex]l(PT) = \sqrt{((1--5)^{2}+(8--7)^{2} )}\\l(PT) = \sqrt{((1+5)^{2}+(8+7)^{2} )}\\l(PT) = \sqrt{((6)^{2}+(15)^{2} )}\\l(PT) = \sqrt{261}\\l(PT) = 16.16\ units[/tex]
And
[tex]l(OT) = \sqrt{((x_{3}-x_{2})^{2}+(y_{3}-y_{2})^{2} )}\\l(OT) = \sqrt{((6-1)^{2}+(6-8)^{2} )}\\l(OT) = \sqrt{((5)^{2}+(-2)^{2} )}\\l(OT) = \sqrt{29}\\l(OT) = 5.39\ units[/tex]
Now substituting OT and PT in area formula we get
[tex]\textrm{Area of Triangle TOP} = \frac{1}{2}\times 5.39\times 16.16\\\textrm{Area of Triangle TOP} = 43.55\ units^{2}[/tex]
Therefore, Area of Δ TOP is 43.55 units².
