Question

Find a point N on the segment with endpoints K(-2, -3) and L(4,3) that partitions thesegment, starting at point K, 1/3 of the way to point L.

Answer 1

First find the length of the segment KL

Apply the formula for distance between two points as;

d = √{y2-y1}^2 + {x2-x1}^2 where

y1= -3 , y2 = 3 , x1 = -2 and x2 = 4

d= √ {3--3}^2 + { 4--2}^2

d= √ 9^2 + 6^2

d= √ 81 + 12

d= √93 = 9.6

So the length of the segment is 9.6

From point K {-2, -3} , find 1/3 of the length to locate point L

This will be : 1/3 * 9.6 =3.2

This means point L is 3.2 units from point K, now apply the distance formula to find x and y coordinates for L, where K is {-2,-3} and L {x,y}

d = √{y2-y1}^2 + {x2-x1}^2

3.2 = √{y--3}^2 + {x--2}^2

3.2 =√ {y+3}^2 +{x+2}^2

3.2^2 = {y+3}^2 + {x+2}^2

10.3 = y^2 + 6y + 9 + x^2 +4x +4

10.3 = y^2 + 6y +x^2 +4x +9+4

10.3 = y^2 + 6y +x^2 +4x +13

0=y^2 +6y +x^2 +4x +13-10.3

0= y^2 +6y +x^2 +4x +2.7

y^2 + 6y +x^2 +4x +2.7 = 0

{-0.9,-0.5)