Advertisements
Advertisements
प्रश्न
Check whether (5, -2), (6, 4) and (7, -2) are the vertices of an isosceles triangle.
Advertisements
उत्तर
Let the points (5, −2), (6, 4), and (7, −2) are representing the vertices A, B, and C of the given triangle respectively.
AB = `sqrt((5-6)^2+(-2-4)^2)`
= `sqrt((-1)^2+(-6)^2)`
= `sqrt(1+36)`
= `sqrt37`
BC = `sqrt((6-7)^2+(4-(-2))^2)`
= `sqrt((-1)^2+(6)^2)`
= `sqrt(1+36)`
= `sqrt37`
CA = `sqrt((5-7)^2+(-2-(-2))^2)`
= `sqrt((-2)^2+0^2)`
= `sqrt(4+0)`
= 2
Therefore, AB = BC ≠ CA
As two sides are equal in length, therefore, ABC is an isosceles triangle.
APPEARS IN
संबंधित प्रश्न
Show that four points (0, – 1), (6, 7), (–2, 3) and (8, 3) are the vertices of a rectangle. Also, find its area
Prove that the points (–3, 0), (1, –3) and (4, 1) are the vertices of an isosceles right angled triangle. Find the area of this triangle
If the points (2, 1) and (1, -2) are equidistant from the point (x, y), show that x + 3y = 0.
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.
If the point A(x,2) is equidistant form the points B(8,-2) and C(2,-2) , find the value of x. Also, find the value of x . Also, find the length of AB.
Determine whether the points are collinear.
L(–2, 3), M(1, –3), N(5, 4)
Find x if distance between points L(x, 7) and M(1, 15) is 10.
Find the distance of a point (12 , 5) from another point on the line x = 0 whose ordinate is 9.
Prove that the points (0,3) , (4,3) and `(2, 3+2sqrt 3)` are the vertices of an equilateral triangle.
Find the distance between the points (a, b) and (−a, −b).
Find the distance between the origin and the point:
(-5, -12)
The distances of point P (x, y) from the points A (1, - 3) and B (- 2, 2) are in the ratio 2: 3.
Show that: 5x2 + 5y2 - 34x + 70y + 58 = 0.
By using the distance formula prove that each of the following sets of points are the vertices of a right angled triangle.
(i) (6, 2), (3, -1) and (- 2, 4)
(ii) (-2, 2), (8, -2) and (-4, -3).
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).
Show that the point (11, – 2) is equidistant from (4, – 3) and (6, 3)
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 distance between the points A(0, 6) and B(0, –2) is ______.
The points (– 4, 0), (4, 0), (0, 3) are the vertices of a ______.
∆ABC with vertices A(–2, 0), B(2, 0) and C(0, 2) is similar to ∆DEF with vertices D(–4, 0), E(4, 0) and F(0, 4).
If (a, b) is the mid-point of the line segment joining the points A(10, –6) and B(k, 4) and a – 2b = 18, find the value of k and the distance AB.
