Rectangle ABCD has a perimeter represented by the expression 9x + 3. Rectangle PQRS has a
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Imagine you're moving along the segment. Since the midpoint is in the middle of the segment (obviously), it means that when you've traveled from G to A, you're halfway through your journey, along both x and y directions. So, let's break the problem in two and analyze both directions.
Along the x axis, you've moved from -3 to 1, so you moved 4 units forward. This means that you have 4 units still to go, and your journey will end at coordinate 5.
Similarly, along the y axis, you've moved from 5 to -4, so you moved 9 units downward. This means that you have 9 units still to go, and your journey will end at coordinate -13.
So, the coordinates of the endpoint are
If you prefer a more analyitical approach, simply write the definition of the midpoint and solve it for the coordinates of T.
We have and
. The midpoint is computed as
So, you have the equations
Multply both equations by 2 to get
Move the constants to the right hand sides to get
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Two cones have their heights in the ratio 1 : 3 and the radius of their bases in the ratio 3 : 1 show that their volumes are in the ratio 3 : 1.
<h2>⇒ Ratio of heights of two cones = 1 : 3
⇒ Ratio of radius of their bases = 3 : 1
⇒ We know that V = 1/3πr²h
⇒ Ratio of their volume = V1 : V2