English

Without Using Distance Formula, Show that the Points A(12,8), B(-2,6) and C(6,0) Form a Right-angled Triangle. - Mathematics

Advertisements
Advertisements

Question

Without using distance formula, show that the points A(12,8), B(-2,6) and C(6,0) form a right-angled triangle.
Sum

Solution

Slope of AB (m1) = `(6 - 8)/(-2 - 12) = (-2)/(-14) = 1/7`

Slope of BC (m2) = `(0 - 6)/(6 + 2) = (-3)/4`

Slope of AC (m3) = `(0 - 8)/(6 - 12) = (-8)/(-6) = 4/3`

Slope of BC x Slope of AC = m2 x m3

                                          = `(-3)/4 xx 4/3`           

                                         = -1

`therefore` AC and BC are perpendicular to each other and ABC form a right angled traiangle.

shaalaa.com
Simple Applications of All Co-ordinate Geometry.
  Is there an error in this question or solution?
Chapter 13: Equation of A Straight Line - Exercise 13.2

APPEARS IN

Frank Mathematics - Part 2 [English] Class 10 ICSE
Chapter 13 Equation of A Straight Line
Exercise 13.2 | Q 17

RELATED QUESTIONS

In the given figure ABCD is a rectangle. It consists of a circle and two semi-circles each of
which are of radius 5 cm. Find the area of the shaded region. Give your answer correct to
three significant figures


Three vertices of parallelogram ABCD taken in order are A(3, 6), B(5, 10) and C(3, 2)

1) the coordinate of the fourth vertex D

2) length of diagonal BD

3) equation of the side AD of the parallelogram ABCD


Using a graph paper, plot the points A(6, 4) and B(0, 4).

  1. Reflect A and B in the origin to get the images A' and B'.
  2. Write the co-ordinates of A' and B'.
  3. State the geometrical name for the figure ABA'B'.
  4. Find its perimeter.

A straight line passes through the points P(–1, 4) and Q(5, –2). It intersects the co-ordinate axes at points A and B. M is the mid-point of the segment AB. Find:

  1. The equation of the line.
  2. The co-ordinates of A and B.
  3. The co-ordinates of M.

(1, 5) and (–3, –1) are the co-ordinates of vertices A and C respectively of rhombus ABCD. Find the equations of the diagonals AC and BD.


Show that A(3, 2), B(6, −2) and C(2, −5) can be the vertices of a square.

  1. Find the co-ordinates of its fourth vertex D, if ABCD is a square.
  2. Without using the co-ordinates of vertex D, find the equation of side AD of the square and also the equation of diagonal BD.

P(3, 4), Q(7, –2) and R(–2, –1) are the vertices of triangle PQR. Write down the equation of the median of the triangle through R.


Point A and B have co-ordinates (7, −3) and (1, 9) respectively. Find:

  1. the slope of AB.
  2. the equation of perpendicular bisector of the line segment AB.
  3. the value of ‘p’ of (−2, p) lies on it.

Use a graph sheet for this question. 
Take 1 cm = 1 unit along both x and y axis.
(i) Plot the following points:
      A(0,5), B(3,0), C(1,0)  and  D(1,–5)
(ii) Reflect the points B, C and D on the y axis and name them as  B',C'andD' respectively.
(iii) Write down the coordinates of B',C 'and D'
(iv) Join the point A, B, C, D, D ', C ', B', A in order and give a name to the closed figure ABCDD'C'B


Use a graph sheet for this question, take 2 cm = 1 unit along both x and y-axis:

  1. Plot the points A (3, 2) and B (5, 0). Reflect point A on the y-axis to A΄. Write co-ordinates of A΄.
  2. Reflect point B on the line AA΄ to B΄. Write the co-ordinates of B΄.
  3. Name the closed figure A’B’AB.

Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×