Answer:
The other midpoint is located at coordinates (-9,-2) (Second option)
Step-by-step explanation:
<u>Midpoints</u>
If P(a,b) and Q(c,d) are points in 
, the midpoint between them is the point exactly in the center of the line that joins P and Q. Its coordinates are given by
We are given one endpoint at P(1,-2) and the midpoint at M(-4,-2). The other endpoint must be at an equal distance from the midpoint as it is from P. We can see both given points have the same value of y=-2. This simplifies the calculations because we only need to deal with the x-coordinate.
The x-distance from P to M is 1-(-4)=5 units. This means the other endpoint must be 5 units to the left of M:
x (other endpoint)= - 4 - 5 = - 9
So the other midpoint is located at (-9,-2) (Second option)
Answer:
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Answer:
Her new monthly payment is now $1,378.91¢
Step-by-step explanation:
For us to calculate the new monthly mortgage payment that Anna will start paying from now on, we need to input the formula for calculating monthly mortgage payments.
The formula is:-
![M = P [\frac{r(1+r)^{n} }{(1+r)^{n}-1}]](https://tex.z-dn.net/?f=M%20%3D%20P%20%5B%5Cfrac%7Br%281%2Br%29%5E%7Bn%7D%20%7D%7B%281%2Br%29%5E%7Bn%7D-1%7D%5D)
Where M is the monthly mortgage payment.
P is the principal
r is the monthly interest rate calculated by dividing your annual interest rate by 12
n is the number of payments(the number of months you will be paying the loan).
In this case, the new principal that Anna must pay back is $231,905.47¢. The annual interest rate has been reduced to 5.17% from 5.75% so the new monthly interest rate will be obtained by dividing the new annual interest rate by 12
= 5.17%/2
= 0.431%
This is the new monthly interest rate.
Since she has been paying her mortgage loan diligently for 5 complete years. It means she now has just 25 years to complete the payment. If 12 months make up one year, then there are - 12 × 25 = 300 more months to go.
300 is therefore "n" that is required for the calculation.
All the terms needed for the calculation of her new monthly mortgage is now complete.
P = $231,905.47¢
r = 0.431%
n = 300
![M = 231,905.47[\frac{0.00431(1+0.00431)^{300} }{(1+0.00431)^{300} -1}]](https://tex.z-dn.net/?f=M%20%3D%20231%2C905.47%5B%5Cfrac%7B0.00431%281%2B0.00431%29%5E%7B300%7D%20%7D%7B%281%2B0.00431%29%5E%7B300%7D%20-1%7D%5D)
![= 231,905.47[\frac{0.00431(3.634)}{2.634}]](https://tex.z-dn.net/?f=%3D%20231%2C905.47%5B%5Cfrac%7B0.00431%283.634%29%7D%7B2.634%7D%5D)
= 231,905.47 × 0.005946
M = $1,378.91¢
Therefore her new monthly mortgage payment will become $1,378.91¢
When Sam is 13 his mother will be 39 which is 3 times as old as he is. So Sam's mother will be 3 times as old as Sam will be in 11 years. (Your answer is 11 years.)
