Question

The triangle formed by the lines y = x, y = 1 - x and x = 0 in a two-dimensional plane is (x and y axes have the
same scale)
a. isosceles and right-angled.
b. isosceles but not right-angled.
C. right-angled but not isosceles.
d. neither isosceles nor right-angled.


Plz answer with explanation ​

Answer 1

Answer:

Option A:

If we take (0,0) as one of the vertices, then by taking integral coordinates on x-axis and y-axis, we can form right-angled triangles. For example (0,0),(3,0),(0,5) will form a right angled triangle.

Hence, option A is possible,

Option B:

Let (x

1

,y

1

),(x

2

,y

2

),(x

3

,y

3

) are the coordinates of the three vertices.

Then area is given by

∣

∣

∣

∣

∣

∣

∣

∣

1

x

1

y

1

1

x

2

y

2

1

x

3

y

3

∣

∣

∣

∣

∣

∣

∣

∣

.

If all the coordinates are integers then the value of the above determinant is a rational number.....(1)

Now, if the above triangle is an equilateral triangle, then area can also be expressed as

4

3

×side

2

For integer coordinates side

2

will be a positive integer. Hence

4

3

×side

2

is an irrational number....(2).

Since (1) and (2) contradict each other, the triangle can not be equilateral.

Option C:

Again we can take (0,0) and (4,0) as two points and any third point on x=2 will form an isosceles triangle along with (0,0) and (4,0). For example: (0,0), (4,0) and (2,6) will form an isosceles triangle.

Hence, option C is possible.

Answered By

Step-by-step explanation:

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