A straight line PQ cuts the x andy axis at M and N respectively. If the points A(-3,5) and B(4,7) lies on PQ , calculate
1.The co ordinate of M and N
2.the area of ∆OMN correct to the nearest whole number
Answers
Answer:
Step-by-step explanation:
Solution :-
Given that
A straight line PQ cuts the x andy axis at M and N respectively.
The points A(-3,5) and B(4,7) lies on PQ.
It implies,
The gradient or slope of PQ is same as that of AB.
The equation of PQ is same as that equation of AB.
We know,
Slope of line joining the points (a, b) and (c, d) is represented by m and is evaluated as
Here, points are A (- 3, 5) and B (4, 7).
Thus,
Gradient of line segment joining A and B is
Hence,
Now,
We know that
Equation of line passes through the point (a, b) and having gradient 'm' is given by
Thus,
Equation of line AB passes through the point (- 3, 5) having slope 2/7 is
So,
Equation of line PQ is
Additional Information
Additional Information Different forms of equations of a straight line
1. Equations of horizontal and vertical lines
Equation of the lines which are horizontal or parallel to the X-axis is y = a, where a is the y – coordinate of the points on the line.
Similarly, equation of a straight line which is vertical or parallel to Y-axis is x = a, where a is the x-coordinate of the points on the line
2. Point-slope form equation of line
Consider a non-vertical line L whose slope is m, A(x,y) be an arbitrary point on the line and P(a, b) be the fixed point on the same line. Equation of line is given by y - b = m(x - a)
3. Slope-intercept form equation of line
Consider a line whose slope is m which cuts the Y-axis at a distance ‘a’ from the origin. Then the distance a is called the y– intercept of the line. The point at which the line cuts y-axis will be (0,a). Then equation of line is given by y = mx + a.
4. Intercept Form of Line
Consider a line L having x– intercept a and y– intercept b, then the line passes through X– axis at (a,0) and Y– axis at (0,b). Equation of line is given by x/a + y/b = 1.
5. Normal form of Line
Consider a perpendicular from the origin having length p to line L and it makes an angle β with the positive X-axis. Then, the equation of line is given by x cosβ + y sinβ = p.
Answer:
Solution :-)
Given that
A straight line PQ cuts the x andy axis at M and N respectively.
The points A(-3,5) and B(4,7) lies on PQ.
It implies,
The gradient or slope of PQ is same as that of AB.
The equation of PQ is same as that equation of AB.
We know,
Slope of line joining the points (a, b) and (c, d) is represented by m and is evaluated as
Here, points are A (- 3, 5) and B (4, 7).
Thus,
Gradient of line segment joining A and B is
Hence,
Now,We know that
Equation of line passes through the point (a, b) and having gradient 'm' is given by
Thus,
Equation of line AB passes through the point (- 3, 5) having slope 2/7 is
So,
Equation of line PQ is
Additional Information
Additional Information Different forms of equations of a straight line
1. Equations of horizontal and vertical lines
Equation of the lines which are horizontal or parallel to the X-axis is y = a, where a is the y – coordinate of the points on the line.
Similarly, equation of a straight line which is vertical or parallel to Y-axis is x = a, where a is the x-coordinate of the points on the line
2. Point-slope form equation of line
Consider a non-vertical line L whose slope is m, A(x,y) be an arbitrary point on the line and P(a, b) be the fixed point on the same line. Equation of line is given by y - b = m(x - a)
3. Slope-intercept form equation of line
Consider a line whose slope is m which cuts the Y-axis at a distance ‘a’ from the origin. Then the distance a is called the y– intercept of the line. The point at which the line cuts y-axis will be (0,a). Then equation of line is given by y = mx + a.
4. Intercept Form of Line
Consider a line L having x– intercept a and y– intercept b, then the line passes through X– axis at (a,0) and Y– axis at (0,b). Equation of line is given by x/a + y/b = 1.
5. Normal form of Line
Consider a perpendicular from the origin having length p to line L and it makes an angle β with the positive X-axis. Then, the equation of line is given by x cosβ + y sinβ = p.
Step-by-step explanation: