NCERT - miscellaneous exercise ch 10 Q-17
The end points of the hypotenuse of a right angled triangle are (1,3) and (-4,1). Find the equation of the legs of the triangle.
Here is the answer to your query.
Let the coordinates of the point of intersection of the remaining two legs of triangle by (x, y)
Now AB ⊥ BC
⇒ Slope of AB × slope of BC = –1
[Note: Locus of B is a circle with centre at and radius . Equation of circle will be shady in next chapter.]
Let (α,β) be a point satisfying the equation (1), In this case,
Equation of AB = y –3 =
and equation of BC is y – 1 =
the answer as given in NCERT is x=1 and y=1. also, the concept of circle has not been introduced in the current chapter so we can't use that concept while solving questions of this chapter. but if u can provide the solution even by it then its fine as i have already read it.
our sir told us a trick at school.
that since the lines are perpendicular we can assume that the slope of one of the line is 0 and that of the other is 1/0.(i.e. htey both are parallel to the respective coordinate axis,but he failed to provide any justification for it) then the equation o the two lines will be
but i need the correct explanation for this assumption. becoz i think we just can't take it to be parallel to the coordinate axis.
The point (α, β) satisfying equation (1) represents the coordinates of the intersection of the legs.
It can be clearly shown that (α, β) = (1, 1) satisfies the equation (1).
In this case, equation of the line (leg) passing through A (1, 3) and B (1, 1) is x = 1.
Equation of the line (leg) passing through B (1, 1) and A (-4, 1) is y = 1.
Hope, you can capture the proper concept.