Coordinate Geometry-Finding ratio of a point splitting a line
Coordinate Geometry
Question: In what ratio is the line joining the points (4,2) and (3,-5) divided by the x-axis? Also, find the coordinates of the point of intersection.
Solution: Let the required ratio be(K:1) and the point on the x-axis be (x,0).
Taking (4,2)=(x1:y1) and (3,-5)=(x2:y2)
Since, y=(ky1+y1)/(k+1)
The ratio of m:n is 2:5 and the value of x is 26/7
(I am sorry that i am unable to use subscript in this web page)
My question is y is the solution using K:1 as the ratio. Secondly why is the solution starting with solving the value of Y (ordinate) and not X.
Kindly help.
Question: In what ratio is the line joining the points (4,2) and (3,-5) divided by the x-axis? Also, find the coordinates of the point of intersection.
Solution: Let the required ratio be(K:1) and the point on the x-axis be (x,0).
Taking (4,2)=(x1:y1) and (3,-5)=(x2:y2)
Since, y=(ky1+y1)/(k+1)
The ratio of m:n is 2:5 and the value of x is 26/7
(I am sorry that i am unable to use subscript in this web page)
My question is y is the solution using K:1 as the ratio. Secondly why is the solution starting with solving the value of Y (ordinate) and not X.
Kindly help.
SOLUTION
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ASKER
d-glitch and aburr, thank you both for your comments.
The attached includes the diagram and the workings.
For now i will not argue with why Y has been chosen instead of X. But can you help me understand why K:1 (that is one in alpha and the other in numeric) has been used instead of m:n ratio.
Thank you
*I did not understand this statement: so the x intercept is 3 + the ratio of the one x unit to get to 4. Your diagram will tell you how to do it.
( 3 + 5/7 = the 26/7 value of x which you got
IMG_4007-coordinate-g.JPG
The attached includes the diagram and the workings.
For now i will not argue with why Y has been chosen instead of X. But can you help me understand why K:1 (that is one in alpha and the other in numeric) has been used instead of m:n ratio.
Thank you
*I did not understand this statement: so the x intercept is 3 + the ratio of the one x unit to get to 4. Your diagram will tell you how to do it.
( 3 + 5/7 = the 26/7 value of x which you got
IMG_4007-coordinate-g.JPG
ASKER CERTIFIED SOLUTION
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And you need to remember that the equation for the x-axis is y=0.
So there are two units of the line above the x-axis and five below.
Complete the big right triangle [with sidebar x=4 and y=-5] to calculate the ratios.