Question

the coordinates of vertices a and b are 0,0and 36,15respectively .if the coordinates of c are integers then what is the minimum area the triangle ABC can have​

Answer 1

minimum area the triangle ABC  = 3/2  sq units  if the coordinates of vertices a and b are 0,0and 36,15respectively

Step-by-step explanation:

Let say coordinate c = ( x, y)

a  = (0, 0)  & b ( 36, 15) & c = ( x, y)

Area of Triangle = (1/2) |  0(15 - y)  + 36(y - 0)  + x(0 - 15)|

= (1/2) | 36y - 15x|

= 3/2 | 12y - 5x |

x & y are integers

for minimum Area  12y - 5x  should be be minimum

as x & y are integers

=> minimum |12y - 5x | = 1

for example y = 2  & x  = 5    or y = 3  x = 7

minimum area the triangle ABC  = (3/2) * 1 = 3/2  sq units

Learn More

If the vertices of the triangle are (1,k), (4,-3), (-9,7) and its area is 15 sq. units, find the value of k.

https://brainly.in/question/1086640

Answer 2

Question⤴

1. ........1
2. ..... 2
3. ...... 3/2
4. ...... 5/2

answer

3/2