# 51. Q(3, 9), P(-1,5)find the coordinates of the missing endpoint if P is the midpoint of NQ

Midpoint formula= (?,?)= (x1+x2/2 , y1+y2/2)
-2= 3+? Making ?= -5
10= 9+? Making ?= 1

The coordinates of the missing endpoint, if P is the midpoint of segment NQ, are found using the formula N = 2P - Q. Substituting the given values into this formula, the coordinates of the missing point N are (-5, 1).

### Explanation:

If point P is the midpoint of segment NQ, we can use the formula for finding the coordinates of the endpoint if we know the midpoint and one endpoint. The formula states:

To find the missing endpoint (in this case, point N), we use the formula: N = 2P - Q

Substituting the given values into the formula, we get:

N = 2(-1, 5) - (3, 9)

N = (-2, 10) - (3, 9)

N = (-5, 1)

So, the coordinates of the missing endpoint N are (-5, 1).

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Daren is 3 years older than Tom. 3 years ago Leah will be 14 less than 3 times Darren's age. 5 years ago, Leah was 2 years less than 2 times Tom. How old will Leah be 4 years from now?

5

set up equations

daren is 3 years older than tom

D = 3 + T

3 years ago leah will be 14 less than 3 times darren's age

L - 3 = 3(D - 3) - 14

L - 3 = 3D - 9 - 14

L = 3D - 9 - 14 + 3

L = 3D - 20

5 years ago, leah was 2 years less than 2 times tom

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find leah's current age

set L = 3D - 20 and L = 2T - 7 equal to each other

3D - 20 = 2T - 7

plug 3 + T into D using the equation D = 3 + T

3D - 20 = 2T - 7

3(3 + T) - 20 = 2T - 7

9 + 3T - 20 = 2T - 7

T = - 7 - 9 + 20

T = 4

plug T back into L = 2T - 7 to find leah's current age

L = 2T - 7

L = 2 * 4 - 7

L = 8 - 7

L = 1

leah's age 4 years from now

add 4 to leah's current age

1 + 4 = 5