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The straight lines x + y = 0 , 3x + y – 4 = 0 , x + 3y – 4 = 0 form a triangle which is
- a)equilateral
- b)right angled
- c)isosceles
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The straight lines x + y = 0 , 3x + y – 4 = 0 , x + 3y – 4...
Since none of the lines are perpendicular therefore it is not a right angled triangle.
now find the intersection points of x+y=0, 3x+y-4=0, x+3y-4=0, we get
(2,-2),(-2,2) & (1,1)
let A(2,-2) B(-2,2), C(1,1)
By distance formula we get AC=AB but not equal to AB therefore it is a isoscels triangle.
so option C is correct
Most Upvoted Answer
The straight lines x + y = 0 , 3x + y – 4 = 0 , x + 3y – 4...
Explanation:
To determine the type of triangle formed by the given lines, we need to find the slopes of the lines and analyze their relationships.
1. Finding the slopes of the lines:
- The equation x - y = 0 can be rewritten as y = x. The slope of this line is 1.
- The equation 3x - y - 4 = 0 can be rewritten as y = 3x - 4. The slope of this line is 3.
- The equation x - 3y - 4 = 0 can be rewritten as y = (1/3)x - 4/3. The slope of this line is 1/3.
2. Analyzing the slopes:
- If the slopes of two lines are equal, then the lines are parallel.
- If the slopes of two lines are negative reciprocals of each other, then the lines are perpendicular.
- If none of the above conditions are satisfied, then the lines are neither parallel nor perpendicular.
Comparing the slopes:
- The slopes of the lines y = x and y = (1/3)x - 4/3 are not equal and not negative reciprocals of each other.
- The slopes of the lines y = x and y = 3x - 4 are not equal and not negative reciprocals of each other.
- The slopes of the lines y = (1/3)x - 4/3 and y = 3x - 4 are also not equal and not negative reciprocals of each other.
3. Determining the type of triangle:
Since none of the slopes are equal or negative reciprocals of each other, the three lines are neither parallel nor perpendicular. Therefore, the triangle formed by these lines is an isosceles triangle.
Answer: C) Isosceles
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The straight lines x + y = 0 , 3x + y – 4 = 0 , x + 3y – 4 = 0 form a triangle which isa)equilateralb)right angledc)isoscelesd)none of theseCorrect answer is option 'C'. Can you explain this answer?
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