Area of Triangle

[goyalsau]

If vertices of a triangle have coordinates (-2,2),(3,2)(x,y), what is the area of the triangle?

1. ||y-2||=1

2. angle at the vertex (x,y) equals 90 degrees

[neerajkumar1_1]

see the attached figure...

points (-2,2) and (3,2) lie on a straight line...

statement 1)

|y-2|=1

this means y=3
or y=1

plotting either of these lines on the graph...
if one notices, any traingle drawn between the given 2 points and a third point on either of these lines...
will form a triangle with the same base and height...
since the base and height will be same... area will remain same for all and we can find it...

Sufficient...

statement 2)
doesnt solve anything by itself...

Pick A

[ksundar]

Yes. Area will remain the same. But without knowing what the x coordinate is, we will not know what the area of the triangle is. Shouldn't the answer be 'E' as we cannot find the answer even using the second clue?

[nisha.menon294]

I think its E too ! OA?

[Fatehdeep Singh]

I do not think we need x coordinate.

Area =b*h/2

Base = Distance between (-2,2) & (3,2)
Height=1(in both cases as described clearly by neerajkumar1_1 in the diagram)

So you can find the area and as we know that area of the triangles with same base and formed within 2 parallel lines is same.
So definite answer can be found using A.
Correct me if i am wrong.

[goyalsau]

I think its E too ! OA?

OA is A,

[ksundar]

The length of the second side can vary between 0 to 1 unless its a straight. If you know what the value of x is, you can probably use the 2nd statement to figure out the length of the two sides.

Please someone explain me how the area can be calculated, just for my understanding. I need some rest before I think about this again!

[Fatehdeep Singh]

Length can vary.But we need height.Height is the perpendicular drawn from the vertex to the base.So if your vertex is anywhere on the line(y=3 or y=1),perpendicular distance(distance between vertex and base) will remain constant(=1 in this case).

[diebeatsthegmat]

If vertices of a triangle have coordinates (-2,2),(3,2)(x,y), what is the area of the triangle?

1. ||y-2||=1

2. angle at the vertex (x,y) equals 90 degrees

double absolute????