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Two points (a , 0) and (0 , b) are joined by a straight line. Another point on this line is
- a)(- 3a , 2b)
- b)(a , - 2b)
- c)(3a , - 2b)
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Two points (a , 0) and (0 , b) are joined by a straight line. Another ...
ing (a,0) to (0,b).
Substituting the x-coordinate of (3a,-2b) into the equation we can find if that point lies on the same line.
For x=3a, the point on the line has
y=(-b/a)(3a)+b=-3b+b=-2b so point (3a,-2b) lies on the same line as the other two points
Most Upvoted Answer
Two points (a , 0) and (0 , b) are joined by a straight line. Another ...
Equation of line x/a + y/b = 1
Given that (a,0) and (0,b) lie on a straight line.
We know that a straight line is represented by y = mx + c
Substituting co-ordinates in equation, we get
(1) 0 = am+c
(2) b=a(0)+c = c
⇒ m = −b/a, c = b
∴ Equation of line is ay=ab−bx
Substituting options we see that (3a,−2b) lies on this line.
Given that (a,0) and (0,b) lie on a straight line.
We know that a straight line is represented by y = mx + c
Substituting co-ordinates in equation, we get
(1) 0 = am+c
(2) b=a(0)+c = c
⇒ m = −b/a, c = b
∴ Equation of line is ay=ab−bx
Substituting options we see that (3a,−2b) lies on this line.
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Community Answer
Two points (a , 0) and (0 , b) are joined by a straight line. Another ...
To find the equation of the line passing through the points (a, 0) and (0, b), we can use the slope-intercept form of a line, which is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Finding the Slope of the Line:
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
m = (y2 - y1) / (x2 - x1)
In this case, the points are (a, 0) and (0, b). Substituting these values into the formula, we get:
m = (b - 0) / (0 - a)
m = b / (-a)
m = -b / a
Finding the y-intercept of the Line:
To find the y-intercept, we can substitute the coordinates of one of the given points into the equation of the line. Let's use the point (a, 0):
0 = (-b / a) * a + c
0 = -b + c
c = b
Therefore, the equation of the line passing through the points (a, 0) and (0, b) is:
y = (-b / a) * x + b
To verify that the point (3a, -2b) lies on this line, we substitute the coordinates of the point into the equation:
-2b = (-b / a) * (3a) + b
-2b = -3b + b
-2b = -2b
Since the equation holds true, the point (3a, -2b) lies on the line.
Hence, the correct answer is option C: (3a, -2b).
y = mx + c
where m is the slope of the line and c is the y-intercept.
Finding the Slope of the Line:
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
m = (y2 - y1) / (x2 - x1)
In this case, the points are (a, 0) and (0, b). Substituting these values into the formula, we get:
m = (b - 0) / (0 - a)
m = b / (-a)
m = -b / a
Finding the y-intercept of the Line:
To find the y-intercept, we can substitute the coordinates of one of the given points into the equation of the line. Let's use the point (a, 0):
0 = (-b / a) * a + c
0 = -b + c
c = b
Therefore, the equation of the line passing through the points (a, 0) and (0, b) is:
y = (-b / a) * x + b
To verify that the point (3a, -2b) lies on this line, we substitute the coordinates of the point into the equation:
-2b = (-b / a) * (3a) + b
-2b = -3b + b
-2b = -2b
Since the equation holds true, the point (3a, -2b) lies on the line.
Hence, the correct answer is option C: (3a, -2b).
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