Advertisements
Advertisements
प्रश्न
Show that the points (2, 0), (– 2, 0) and (0, 2) are vertices of a triangle. State the type of triangle with reason
उत्तर
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.
APPEARS IN
संबंधित प्रश्न
If the point P(2, 2) is equidistant from the points A(−2, k) and B(−2k, −3), find k. Also find the length of AP.
If the opposite vertices of a square are (1, – 1) and (3, 4), find the coordinates of the remaining angular points.
Find a relation between x and y such that the point (x, y) is equidistant from the point (3, 6) and (−3, 4).
Given a line segment AB joining the points A(–4, 6) and B(8, –3). Find
1) The ratio in which AB is divided by y-axis.
2) Find the coordinates of the point of intersection.
3) The length of AB.
Find the value of a when the distance between the points (3, a) and (4, 1) is `sqrt10`
Find the circumcenter of the triangle whose vertices are (-2, -3), (-1, 0), (7, -6).
Find the centre of the circle passing through (6, -6), (3, -7) and (3, 3)
Two opposite vertices of a square are (-1, 2) and (3, 2). Find the coordinates of other two
vertices.
Find the distance between the following pair of point in the coordinate plane :
(5 , -2) and (1 , 5)
Find the distance of the following point from the origin :
(8 , 15)
Find the distance of a point (12 , 5) from another point on the line x = 0 whose ordinate is 9.
Prove that the points (4 , 6) , (- 1 , 5) , (- 2, 0) and (3 , 1) are the vertices of a rhombus.
Find the distance between the origin and the point:
(8, -15)
If the length of the segment joining point L(x, 7) and point M(1, 15) is 10 cm, then the value of x is ______
Find distance of point A(6, 8) from origin
If the distance between point L(x, 7) and point M(1, 15) is 10, then find the value of x
Using distance formula decide whether the points (4, 3), (5, 1), and (1, 9) are collinear or not.
AOBC is a rectangle whose three vertices are A(0, 3), O(0, 0) and B(5, 0). The length of its diagonal is ______.
Name the type of triangle formed by the points A(–5, 6), B(–4, –2) and C(7, 5).
Show that Alia's house, Shagun's house and library for an isosceles right triangle.
