CHALLENGE TO ALL THOSE WHO ARE SCHOLAR IN MATHEMATICS-
Two lines 6y=5x+10 and y=5x-15 meet at (4,5) find the area of the triangle between the two lines and the x axis (answer with full method will be marked as brainliest)it is from coordinate geometry class 9
Answers
ans is 30 sq. units
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Answer:
12.5 cm²
Step-by-step explanation:
Good question.
Consider the line 6y = 5x + 10.
Let y = 0, to find the point where this line meets the x axis.
6 × 0 = 5x + 10
5x + 10 = 0
x = - 10 / 5
x = -2
∴ This line meets the x axis at (-2, 0). Let this point be A.
Consider the line y = 5x - 15.
Let y here also be 0, to find the point where this line also meets the x axis.
0 = 5x - 15
5x = 15
x = 3
∴ This line meets the x axis at (3, 0). Let this point be B.
Let the point (4, 5) where the two lines meet each other be C.
So we've to find the area of ΔABC.
For this, we've to find the altitude corresponding to the x axis.
This altitude is from C, i.e., (4, 5), to AB, which belongs to x axis.
As this altitude meets the x axis, the y coordinate of the point where this altitude meets the x axis becomes 0.
As this altitude is perpendicular to x axis, this becomes parallel to y axis, and therefore, the x coordinate of the point where this altitude meets the x axis becomes equal to that of (4, 5).
So the point where this altitude meets the x axis is (4, 0). Let this point be M, so that the altitude becomes CM.
So let's find the length of the altitude, i.e., distance between points (4, 5) and (4, 0).
CM = √((4 - 4)² + (5 - 0)²)
CM = √(0² + 5²)
CM = √25
CM = 5
∴ Length of CM is 5.
Okay, then we need the length of AB to which the altitude is drawn.
So let's find the distance between points (-2, 0) and (3, 0). (I.e., AB)
AB = √((-2 - 3)² + (0 - 0)²)
AB = √((-5)² + 0²)
AB = √25
AB = 5
∴ So, AB is also 5.
NOW LET'S FIND THE AREA OF ΔABC!!!
1/2 × AB × CM
1/2 × 5 × 5
1/2 × 25 = 12.5
∴ Area of the triangle is 12.5 unit².
Hence it's found!
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Hope this may be helpful.
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The responsible figure is also attached with the answer.
Actually I answered this yesterday and all was set, but unfortunately the answer couldn't be posted and when I reloaded the page copying my answer, my chance to answer lost!!! Now I got it.
But, even I answered this, I won't be a mathematical genius!!! (Please see my profile if you don't believe this!!!) ;-P
Thank you. Have a nice day. :-))
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