the ratio in which the line segment is joining A(2,7) B(4,-7) is divided by x-axis is the ratio in which the line segment is joining A(2,7) B(4,-7) is divided by x-axis is
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Mathematics
Science
Chapters in Mathematics Exemplar Problems - class 10
Exercises in Coordinated Geometry
Question 5
In what ratio does the x–axis divide the line segment joining the points (– 4, – 6) and (–1, 7)? Find the coordinates of the point of division.
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Let the ratio in which x-axis divides the line segment joining (–4, –6) and (–1, 7) = 1: k.
Then,
x-coordinate becomes (-1 – 4k) / (k + 1)
y-coordinate becomes (7 – 6k) / (k + 1)
Since P lies on x-axis, y coordinate = 0
(7 – 6k) / (k + 1) = 0
7 – 6k = 0
k = 7/6
Therefore, the point of division divides the line segment in the ratio 6 : 7.
Now, m1 = 6 and m2 = 7
By using section formula,
x = (m1x2 + m2x1)/(m1 + m2)
= (6(-1) + 7(-4))/(6+7)
= (-6-28)/13
= -34/13
So, now
y = (6(7) + 7(-6))/(6+7)
= (42-42)/13
= 0
Hence, the coordinates of P are (-34/13, 0)
Step-by-step explanation:
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Answer:
x-coordinate becomes (-1 – 4k) / (k + 1)
y-coordinate becomes (7 – 6k) / (k + 1)
Since P lies on x-axis, y coordinate = 0
(7 – 6k) / (k + 1) = 0
7 – 6k = 0
k = 7/6
Therefore, the point of division divides the line segment in the ratio 6 : 7.
Now, m1 = 6 and m2 = 7
By using section formula,
x = (m1x2 + m2x1)/(m1 + m2)
= (6(-1) + 7(-4))/(6+7)
= (-6-28)/13
= -34/13
So, now
y = (6(7) + 7(-6))/(6+7)
= (42-42)/13
= 0
Hence, the coordinates of P are (-34/13, 0)