maths

P(6,3), Q(3,7), and R(4,2) are three points in a plane. A is the midpoint of QR and B is the foot of the perpendicular from Q to PR. Find;-
(A) the cordinates of A;
(B) the equations of the lines PA and QB;
(C) the point of intersection of the lines PA and QB;
(D) the equation of the line passing through Q and parallel to the line PR.

need help I don't understand it

  1. 👍
  2. 👎
  3. 👁
  1. Midpoint is (x1 + x2)/2, (y1 + y2)/2
    Label your coordinates (x1, y1) and (x2, y2)
    and begin : )

    1. 👍
    2. 👎
  2. Plot the given points on a Cartesian plane, label them, and join them with a ruler. This helps immensely to see
    what needs to be done.
    a) Find the midpoint A of QR using the formula Ms Pi provided. Use points P and Q.
    b) PA is a median and QR is an altitude. Rough sketch them in. To get the equations of them, use what you know about slopes as well as y = mx + b.
    c) Use substitution or elimination to solve the system of two equations you found in part b).
    d) Rough sketch this line and use what you know about slopes as well as y = mx + b to get its equation.

    1. 👍
    2. 👎
  3. Correction on item a):
    Use points Q and R :)

    1. 👍
    2. 👎
  4. Using the method that Ms Pi told you,
    A is ( (4+3)/2 , (2+7)/2 = A( 7/2,9/2)

    for equation of PA
    slope PA = (9/2-3)/(7/2-6) = -3/5
    so equation: y-3 = (-3/5)(x-6)
    5y - 15 = -3x + 18
    3x + 5y = 33 <--- equation of AP

    slope of PR = (3-2)/(6-4) = 1/2
    slope slope of QB = -2
    equation of QB: y-7 = -2(x-3)
    y-7 = -2x + 6
    2x + y = 13 or y = 13-2x

    sub into 3x + 5y = 33
    3x + 5(13-2x) = 33
    3x + 65 - 10x = 33
    -7x = - 32
    x = 32/7
    back into y = 13 - 2x
    y = 27/7

    The last is straightforward, you do it, let me know what you get

    1. 👍
    2. 👎
    👤
    Reiny

Respond to this Question

First Name

Your Response

Similar Questions

  1. Geometry; Check answers?

    For each graph, find (a)AB to the nearest tenth and (b)the coordinates of the midpoint of AB. 1. Coordinates are A(-9, -6) B(6,6) D=19.2 Midpoint=(1.5,-6) 2.A(-2,-2) B(8,-6) D=10.77 midpoint= (3,-4) 3. A(0,3) B(-2,-2) D=5.4

  2. geometry

    Decide which one of the following statements is false. a. any three points lie on a distinct line. b. three noncollinear points determine a plane. c. a line contains at least two points. d. through any two distinct points there

  3. (Pre-Algebra) A

    Lesson 7: Coordinate Plane Essential Algebra Readiness(Pre-Algebra) A Unit 4: Real Numbers and the Coordinate Plane Has anyone done the Coordinate Plane Practice AND assessment? 1. Which point is located at (-3, -2)? (1 point)

  4. Math - repost

    The angles of elevation θ and ϕ to an airplane are being continuously monitored at two observation points A and B, respectively, which are 5 miles apart, and the airplane is east of both points in the same vertical plane.

  1. MATH (PLZ HELP)

    JK bisects LM at point D which of the following is true about point D? Draw a picture to help you answer the question. A. D is the midpoint of JK B. D is both the midpoint of JK and the midpoint of LM C. D is the midpoint of LM D.

  2. Finding the midpoint

    Find the midpoint of the line segment joining the points P1 and P2 P1=(3,2) P2=(-5,7) The midpoint is=

  3. Math

    How do you find the distance and midpoint between two points in the coordinate plane?

  4. Math

    Any 2 points determine a line. If there are 6 points in a plane, no 3 of which lie on the same line, how many lines are determined by pairs of these 6 points? The answer key says 15, and the explanation is (6!)/(2!4!). Could

  1. math

    Points $P$ and $R$ are located at (2, 1) and (12, 15) respectively. Point $M$ is the midpoint of segment $\overline{PR}$. Segment $\overline{PR}$ is reflected over the $x$-axis. What is the sum of the coordinates of the image of

  2. Math - Equations of plane(check)

    Consider the plane that contains points A(2,3,1), B(-11,1,2), C(-7,-3,-6). a) Find two vectors that are parallel to the plane. Ans: AC, BC or AB will be parallel to the plane. b) Find two vectors that are perpendicular to the

  3. physics

    What percentage of the takeoff velocity did the plane gain when it reached the midpoint of the runway?

  4. math

    Find coordinates for two points that belong to the plane 2x+3y+5z=15. Show that the vector [2,3,5] is perpendicular to the segment that joins your two points. Explain why [2,3,5] is perpendicular to the plane.

You can view more similar questions or ask a new question.