Analytic Geometry

posted by .

Please help. I've been trying to solve these for more than an hour now but I can't seem to get it.

1) The segment joining (-4,7), (5,-2) is divided into two segments, one of which is 5 times as long as the other. Find the point of division.

2) The segment joining (4,0), (3, -2) is extended each way a distance equal to three times its own length. Find the terminal points.

Please show the solutions so I can study them. Thanks in advance :).

  • Analytic Geometry -

    1)
    Naturally, there are two places to make the division: one near (-4,7) and the other near (5,-2)

    Taking the one near (-4,7), we want a point which is 1/6 the way to (5,-2).

    (-4 + 1/6 (5+4),7 + 1/6 (-2-7)) = (-5/2,11/2)

    2)
    in the same way as above, figure the difference between the points and go out 3 times that distance in each direction:

    (4,0) + 3((4-3),(0+2)) = (4,0)+(3,6) = (7,6)

    (3,-2) + 3((3-4),(-2-0)) = (3,-2)+(-3,-6) = (0,-8)

  • Analytic Geometry -

    x= -5/2
    y= 11/2

  • Analytic Geometry -

    #1.
    x=-4 + 5/6(5+4)=7/2
    y=7 + 5/6(-2-7)=-1/2
    P(7/2,-1/2)

  • Analytic Geometry -

    #2.
    x=4 + 3(4-3)=7
    y=0 + 3(0+2)=6
    p(7,6)
    x=3 + 3(3-4)=0
    y=-2 + 3(-2-0)=-8
    p(0,-8)

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math

    A 24-cm segment is divided into two segments. One segment is three times as long as the other. Find the lenghts of both segments.
  2. geometry

    a line segment is divided into two segments that are in a ratio 4 to 7. the measure of one segment is 15 inches longer than the measure of the other. Find the measure of each segment.
  3. geometry

    a line segment is divided into two segments that are in a ratio 4 to 7. the measure of one segment is 15 inches longer than the measure of the other. Find the measure of each segment.
  4. Geometry

    a line segment is divided into two segments that are in a ratio 4 to 7. the measure of one segment is 15 inches longer than the measure of the other. Find the measure of each segment.
  5. Geometry

    a line segment is divided into two segments that are in a ratio 4 to 7. the measure of one segment is 15 inches longer than the measure of the other. Find the measure of each segment.
  6. geometry

    A segment 12" long is divided into two segments having lengths in the ratio of 2:3. Find the length of each segment. (Hint: Let 2x and 3x represent the length of the parts.) x = ?
  7. math

    A circle is divided into four segments from the center of the circle. One segment is x degree and each of the other three segments increases by 20 degree from the previous segment. What is the value of the largest segment?
  8. geometry

    What is scale factor for the dilation of segment AB into segment CD?
  9. Analytic Geometry

    What are the lengths of the segments into which the y-axis divides the segment joining (-6,-6) and (3,6) ?
  10. Geometry

    I have another question that stumped me Line segment AB with length a is divided by points P and Q into three line segments: AP , PQ, and QB , such that AP = 2PQ=2QB. Find: A)the distance between point A and the midpoints of the segments …

More Similar Questions