English
Maharashtra State BoardSSC (English Medium) 10th Standard

Show that the points (2, 0), (– 2, 0) and (0, 2) are vertices of a triangle. State the type of triangle with reason - Geometry Mathematics 2

Advertisements
Advertisements

Question

Show that the points (2, 0), (– 2, 0) and (0, 2) are vertices of a triangle. State the type of triangle with reason

Sum
Advertisements

Solution

Let the points be P(2, 0), Q(– 2, 0) and R(0, 2)

Distance between two points = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`

By distance formula,

d(P, Q) = `sqrt([(-2) - 2]^2 + (0 - 0)^2`

= `sqrt((-4)^2 + (0)^2`

= `sqrt(16 + 0)`

= 4    .....(i)

d(Q, R) = `sqrt([0 - (-2)]^2 + (2 - 0)^2`

= `sqrt((2)^2 + (2)^2`

= `sqrt(4 + 4)`

= `sqrt(8)`  ......(ii)

d (P, R) = `sqrt((0 -2)^2 + (2 - 0)^2`

= `sqrt((- 2)^2 + (2)^2`

= `sqrt(4 + 4)`

= `sqrt(8)`  ......(iii)

On adding (ii) and (iii),

d(P, Q) + d(Q, R) = `4 + sqrt(8)`

`4 + sqrt(8) > sqrt(8)`

∴ d(P, Q) + d(Q, R) > d(P, R)

∴ Points P, Q, R are non colinear points.

We can construct a triangle through 3 non collinear points.

∴ The segment joining the given points form a triangle.

Since P(Q, R) = P(P, R)

∴ ∆PQR is an isosceles triangle.

∴ The segment joining the points (2, 0), (– 2, 0) and (0, 2) will form an isosceles triangle.

shaalaa.com
  Is there an error in this question or solution?
Chapter 5: Co-ordinate Geometry - Q.4

APPEARS IN

RELATED QUESTIONS

If two vertices of an equilateral triangle be (0, 0), (3, √3 ), find the third vertex


Find the coordinates of the centre of the circle passing through the points (0, 0), (–2, 1) and (–3, 2). Also, find its radius.


Find the values of x, y if the distances of the point (x, y) from (-3, 0)  as well as from (3, 0) are 4.


Two opposite vertices of a square are (-1, 2) and (3, 2). Find the coordinates of other two
vertices.


Find all possible values of y for which distance between the points is 10 units.


If A and B are the points (−6, 7) and (−1, −5) respectively, then the distance

2AB is equal to


Find the distance of the following point from the origin :

(13 , 0)


In what ratio does the point P(−4, y) divides the line segment joining the points A(−6, 10) and B(3, −8)? Hence find the value of y.


Find the distance between the origin and the point:
(-8, 6) 


A point P lies on the x-axis and another point Q lies on the y-axis.
Write the abscissa of point Q.


Show that (-3, 2), (-5, -5), (2, -3) and (4, 4) are the vertices of a rhombus.


Show that each of the triangles whose vertices are given below are isosceles :
(i) (8, 2), (5,-3) and (0,0)
(ii) (0,6), (-5, 3) and (3,1).


The distance between point P(2, 2) and Q(5, x) is 5 cm, then the value of x ______


Find distance CD where C(– 3a, a), D(a, – 2a)


Show that A(1, 2), (1, 6), C(1 + 2 `sqrt(3)`, 4) are vertices of a equilateral triangle


AOBC is a rectangle whose three vertices are A(0, 3), O(0, 0) and B(5, 0). The length of its diagonal is ______.


The point which divides the lines segment joining the points (7, -6) and (3, 4) in ratio 1 : 2 internally lies in the ______.


The equation of the perpendicular bisector of line segment joining points A(4,5) and B(-2,3) is ______.


Find a point which is equidistant from the points A(–5, 4) and B(–1, 6)? How many such points are there?


Show that Alia's house, Shagun's house and library for an isosceles right triangle.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×