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1 answer:
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Given
∆PQR points are P(-2,5), Q(-1,1), and R(7,3)
Determine whether ∆PQR is a right triangle
To proof
As given ∆PQR points are P(-2,5), Q(-1,1), and R(7,3)
First find out the sides of triangle
FORMULA
Distance formula between two points
Distance between two points P(-2,5) and Q(-1,1)
Distance between two points Q(-1,1)and R(7,3)
Distance between two points R(7,3) and P(-2,5)
now show that ∆PQR is a right triangle
Putting the value given above
85 = 17 +68
85 =85
In the right triangle
HYPOTENUSE² = BASE² + PERPENDICULAR²
This is prove above
Hence ∆PQR is a right triangle
Hence proved
Answer:
Option C - 9 AU
Step-by-step explanation:
To find : What is the average distance from Planet B to the star?
Solution :
According to kepler's law,
The squares of the sidereal periods (of revolution) of the planets are directly proportional to the cubes of their mean distances from the Sun.
i.e.
We have given,
The average distance from the star to Planet A is AU.
It takes 432 Earth days for Planet A to orbit the star i.e.
It takes 1,460 days for Planet B to complete an orbit i.e.
Substitute the values in
Taking root cube both side,
The average distance from Planet B to the star is 9 AU.
Therefore, Option C is correct.