mikemcgarry wrote:
Archit143 wrote:
ABC is a right angle triangle, right angled at B Co ordinates of A, B and C are (X,Z), (X,Y) and (X+3, Y) respectively. Length of line AC is 5 units, x and y are greater than or equal to 0, the vertices of triangle ABC have coordinate values as shown, and the value of AC is as shown. If x = 3, then what could be the slope of line AC?
A. -4/3
B. 2/3
C. 1
D. 4/3
E. 2
I'm happy to help with this.
We know the hypotenuse AC = 5, and we know BC = 3, because B & C have the same y-coordinate (BC is horizontal) and they are separated in the horizontal direction by 3.
If a right triangle has a hypotenuse of 5 and one leg of 3, the other leg has to be 4. That is the inescapable conclusion of the Pythagorean Theorem. We must have a 3-4-5 triangle.
The trouble is ---- we don't know if Z > Y or Z < Y ---- the problem provides no information on that point. Thus, we have a horizontal segment BC of length 3, with a right angle at B, but we don't know whether the perpendicular segment AB goes up or down from B. We know AB must have a length of 4 and that it must make a right angle with B, but we don't know whether the direction from B to A is up or down. Therefore, the slope of AB could be either +4/3 or -4/3. Two answers are possible here.
I suspect either something was not copied correctly from the source, or that the source is faulty.
Let me know if you have any questions.
Mike
Hi Mike
First of all thanks for replying to my post.... The actual question is to find the equation of AC which is not difficult after we get the slope.
Pls find below the actual question
In the figure to the left, x and y are greater than or equal to 0, the vertices of triangle ABC have coordinate values as shown, and the value of AC is as shown. If x = 3, then what could be the equation of line AC?
The co ordinates remains the same as in the original question.
My doubt is
When we get the 3 - 4 -5 triangle with clear value as 3 , 4 and 5 not as ratio, also from the equation we know that change in y axis (delta Y ) is 4 and that of X axis is 3. why cant we conclude straight away that the slope is 4/3 .
Yes if we substitute the value of Z as y+ 4 than we get - 4/3
Why is it so..............
The solution assumes the value to be - 4/3 and calculates the equation of line.
Question; why is there two possible SLOPE of a single line.........