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Find the point which divides the line joining the points A (1, 3) and B (2, 7) in the ratio of 3 : 4 externally.
- a)(-2, -13)
- b)(-2, 12)
- c)(-6, -13)
- d)(-2, -9)
Correct answer is option 'D'. Can you explain this answer?
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Find the point which divides the line joining the points A (1, 3) and ...
To find the point which divides the line joining the points A(1, 3) and B(2, 7) in the ratio of 3:4 externally, we can use the section formula.
The section formula states that the coordinates of a point dividing a line segment joining two points (x₁, y₁) and (x₂, y₂) in the ratio m:n are given by:
X = (n*x₁ + m*x₂) / (m + n)
Y = (n*y₁ + m*y₂) / (m + n)
In this case, we are given that the ratio is 3:4 externally. This means that the point is 3 units away from A and 4 units away from B.
Let's substitute the given values into the section formula:
X = (4*1 + 3*2) / (3 + 4) = (4 + 6) / 7 = 10 / 7
Y = (4*3 + 3*7) / (3 + 4) = (12 + 21) / 7 = 33 / 7
Therefore, the coordinates of the point that divides the line AB in the ratio 3:4 externally are (10/7, 33/7).
Now, let's check which option matches these coordinates:
a) (-2, -13)
b) (-2, 12)
c) (-6, -13)
d) (-2, -9)
We can see that none of the options match the coordinates (10/7, 33/7) that we calculated.
Hence, none of the given options is the correct answer.
The section formula states that the coordinates of a point dividing a line segment joining two points (x₁, y₁) and (x₂, y₂) in the ratio m:n are given by:
X = (n*x₁ + m*x₂) / (m + n)
Y = (n*y₁ + m*y₂) / (m + n)
In this case, we are given that the ratio is 3:4 externally. This means that the point is 3 units away from A and 4 units away from B.
Let's substitute the given values into the section formula:
X = (4*1 + 3*2) / (3 + 4) = (4 + 6) / 7 = 10 / 7
Y = (4*3 + 3*7) / (3 + 4) = (12 + 21) / 7 = 33 / 7
Therefore, the coordinates of the point that divides the line AB in the ratio 3:4 externally are (10/7, 33/7).
Now, let's check which option matches these coordinates:
a) (-2, -13)
b) (-2, 12)
c) (-6, -13)
d) (-2, -9)
We can see that none of the options match the coordinates (10/7, 33/7) that we calculated.
Hence, none of the given options is the correct answer.
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Find the point which divides the line joining the points A (1, 3) and ...
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