|
Question 176789: Find the point that is one-fourth of the distance from the point P(-1,3) to the point Q(7,5) along the segment PQ
Found 2 solutions by Alan3354, stanbon:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Find the point that is one-fourth of the distance from the point P(-1,3) to the point Q(7,5) along the segment PQ
-------------------
Calculate x and y separately.
diff in x = (7 - (-1)) = 8
diff in y = (5-3) = 2
1/4 of x = 2
1/4 of y = 1/2
Call the point R
Rx = Px + 2 = +1
Ry = Py + 0.5 = 3.5
So R is:
(1,3.5)
Answer by stanbon(75887)  (Show Source):
You can put this solution on YOUR website! Find the point that is one-fourth of the distance from the point P(-1,3) to the point Q(7,5) along the segment PQ
-------------------------------------
Plot the points.
Let PQ be the hypotenuse of a rt. triangle with 3rd point R(7,3)
Find length of PQ: sqrt(8^2+2^2) = sqrt(68) = 2sqrt(17)
(1/4)2sqrt(17) = (1/2)sqrt(17)
-----------------------------------
let a point (1/4)th of the way from P to Q be M(x,y)
Draw a line segment from M perpendicular to PR at N.
--------------
Triangle PMN is proportional to Triangle PQR.
-----
A point (1/4) of the way from P to R is (1,3)
A point (1/4) of the way from R to Q is (7,3 1/2)
------------------
so the point (1/4) of the way from P to Q is (1,(7/2))
------------------
Prove it:
distance from P to Q = sqrt[(1--1)^2 + (3-(7/2)^2] = sqrt[4 + 1/4]
= sqrt[17/4] = (1/2)sqrt(17)
and this is (1/4) the way from P to Q.
===========================================
Cheers,
Stan H.
|
|
|
| |
