English

Show that the Line Joining the Points A(4, 8) and B(5, 5) is Parallel to the Line Joining the Points C(2, 4) and D(1, 7). - Geometry Mathematics 2

Advertisements
Advertisements

Question

Show that the line joining the points A(4, 8) and B(5, 5) is parallel to the line joining the points C(2, 4) and D(1, 7).

Solution

Slope of the line joining the points A(4, 8) and B(5, 5) will be

\[= \frac{5 - 8}{5 - 4} = \frac{- 3}{1} = - 3\]
Slope of the line joining the points C(2, 4) and D(1, 7) will be
\[= \frac{7 - 4}{1 - 2} = \frac{3}{- 1} = - 3\]
Since the slope of AB = slope of CD
so, the given lines are parallel.
shaalaa.com
  Is there an error in this question or solution?
Chapter 5: Co-ordinate Geometry - Problem Set 5 [Page 123]

APPEARS IN

Balbharati Geometry (Mathematics 2) [English] 10 Standard SSC Maharashtra State Board
Chapter 5 Co-ordinate Geometry
Problem Set 5 | Q 10 | Page 123

Video TutorialsVIEW ALL [2]

RELATED QUESTIONS

The slope of a line joining P(6, k) and Q(1 – 3k, 3) is `1/2`. Find:

  1. k.
  2. mid-point of PQ, using the value of ‘k’ found in (i).

The line through P(5, 3) intersects y-axis at Q.

(1) Write the slope of the line.
(2) Write the equation of the line.
(3) Find the coordinates of Q.


Find the slope of the line perpendicular to AB if : A = (3, −2) and B = (−1, 2)


Without using the distance formula, show that the points A(4, 5), B(1, 2), C(4, 3) and D(7, 6) are the vertices of a parallelogram.


(−2, 4), (4, 8), (10, 7) and (11, –5) are the vertices of a quadrilateral. Show that the quadrilateral, obtained on joining the mid-points of its sides, is a parallelogram.


The side AB of a square ABCD is parallel to the x-axis. Find the slopes of all its sides. Also, find: 

  1. the slope of the diagonal AC.
  2. the slope of the diagonal BD.


The line through P(5, 3) intersects y-axis at Q.

  1. Write the slope of the line.
  2. Write the equation of the line.
  3. Find the co-ordinates of Q.


Determine whether the following point is collinear.

P(2, –5), Q(1, –3), R(–2, 3)


If A(1, –1), B(0, 4), C(–5, 3) are vertices of a triangle then find the slope of each side.


Fill in the blank using correct alternative.
Seg AB is parallel to Y-axis and coordinates of point A are (1,3) then co–ordinates of point B can be ........ .


Show that points P(1, –2), Q(5, 2), R(3, –1), S(–1, –5) are the vertices of a parallelogram.


Find the slope of a line, correct of two decimals, whose inclination is 45°


Find the slope of a line parallel to the given line 5x + 2y = 11


Find the slope of a line passing through the following pair of point 

(²m²,2am) and (p²m²,2pm)


Find the value of a line perpendicular to the given line  5x+2y-9 = 0


Find the slope of a line having inclination 60°.


Find the Slope of the line having inclination 45°.


In the figure, line l is parallel to X-axis. Which of the following statement is true?


Determine whether the following points are collinear. A(–1, –1), B(0, 1), C(1, 3)

Given: Points A(–1, –1), B(0, 1) and C(1, 3)

Slope of line AB = `(square - square)/(square - square) = square/square` = 2

Slope of line BC = `(square - square)/(square - square) = square/square` = 2

Slope of line AB = Slope of line BC and B is the common point.

∴ Points A, B and C are collinear.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×