Maths-
General
Easy
Question
If 7x – y + 3 = 0; x + y – 3 = 0 are tow sides of an isosceles triangle and the third side passes through (1, 0) then the equation of the third side is
- x + 3y + 1 = 0
- x – 3y – 1 = 0
- x – 3y + 1 = 0
- x + 3y – 1 = 0
Hint:
Any triangle with any two sides that have the same length is known as an isosceles triangle. An isosceles triangle has two equal-sized angles that are opposite from one other and have equal sides. Here we have given that if 7x – y + 3 = 0; x + y – 3 = 0 are two sides of an isosceles triangle and the third side passes through (1, 0) then what is the equation of the third side.
The correct answer is: x – 3y – 1 = 0
The equation of a line has the following typical forms:
- Form of a slope-intercept
- Normal form
- Intercept form
The first-degree line's general equation in two variables is written as: Ax + By +C = 0.
The equation of any line passing through the given point (1,0) will be:
y - 0 = m(x − 1)
Since it makes equal angle theta with the given lines 7x – y + 3 = 0 and x + y – 3 = 0, therefore
So from this we can say that the two possible equations of third side are:
y - 0 = -3(x − 1)
y = 3 - x
or
y - 0 = -1/3(x − 1)
3y = 1 - x
x + 3y - 1 = 0
So from this we can say that the two possible equations of third side are:
y - 0 = -3(x − 1)
y = 3 - x
or
y - 0 = -1/3(x − 1)
3y = 1 - x
x + 3y - 1 = 0
So here we used the concept of the triangles, and the equations of the lines to solve this problem. We know that the equation of a straight line in slope-intercept form is given as y = mx+c, so we used that here. So the equation of the third side is x + 3y - 1 = 0.
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