Find a Point 3/8 along the LineDate: 12/04/2002 at 21:48:10 From: Daniel Subject: XY graph find a point 3/8 along the line How does one solve this one? Find a point 3/8 from A to B. Given: two endpoints X,Y coordinates Point A (-2, 7) point B (6, -5) The midpoint formula we are using is X1 + X2, Y1 + Y2 midpt (x, y) = -------- ------- 2 2 -2 + 6 , 7 + -5 midpt (x, y) = ------- ------ 2 2 midpt (2, 1) To find 3/8 we used: 3(X1 + X2) 3(X1 + X2) --------- , ---------- 8 8 We get 3/8 point of (3/2, 3/4) The book says it should be (1, 5/2) Where are we messing up? Thanks, Daniel Date: 12/05/2002 at 15:11:19 From: Doctor Ian Subject: Re: XY graph find a point 3/8 along the line Hi Daniel, Plot the two points, | <- 8 -> A.......-........................ | . - . | . - . | . - . | . - . ^ | . | - . 12 | . | - . v | . ---|---|---|---|---|---+---|---|---|---|---|---|---|---|--- | . - . | . - . | . - . | . - . | . - B | - | - | Suppose we want to make a similar triangle, but 3/8 the size of this one. The base would be (3/8)(8), or 3; and the altitude would be (3/8)(12), or 9/2: <- 3 -> | A.......-........................ | . . - . ^ . | . | . - . 9/2 . | . | . - . v . | . . - . . | B' . - . | . - . | . ---|---|---|---|---|---+---|---|---|---|---|---|---|---|--- | . - . | . - . | . - . | . - . | . - B | - | - | So the location of the point you're looking for should be X = X + (3/8)(X - X ) = -2 + (3/8)(8) = -2 + 3 = 1 B' A B A Y = Y + (3/8)(Y - Y ) = 7 + (3/8)(-12) = 7 - 9/2 = 5/2 B' A B A Basically, to go 3/8 of the way along the hypotenuse, you have to go 3/8 of the way along each leg, starting from the initial point. Does this make sense? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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