CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
Question

The points (a, a), (−a, a) and (-3a,3a) form the vertices of

(a) an equilateral triangle
(b) a scalene triangle
(c) an isosceles triangle
(d) a right triangle

Open in App
Solution

(a) an equilateral triangle
Let A(a, a), B(−a, −a) and C-3a, 3a be the given points. Then,
AB=-a-a2+-a-a2 =-2a2+-2a2 =4a2+4a2 =8a2 =22a unitsBC=-3a+a2+3a+a2 =a1-32+1+32 =a21+3 =a8 =22a unitsAC=-3a-a2+3a-a2 =a3+12+3-12 =a23+1 =a8 =22a units
AB = BC = AC
Hence, the points form the vertices of an equilateral triangle.

flag
Suggest Corrections
thumbs-up
1
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Reducing a Triangle to Two Right Angled Triangles
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon