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Find the coordinates of the point which divides P1(1, -4) and P2(4, 2) externally in the ratio 1 : 4.
- a)(0, -6)
- b)(6, -6)
- c)(0, -8)
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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Find the coordinates of the point which divides P1(1, -4) and P2(4, 2)...
To find the coordinates of the point which divides P1(1, -4) and P2(4, 2) externally in the ratio 1:4, we can use the section formula.
The section formula states that if a line segment AB is divided by a point P in the ratio m:n, then the coordinates of P can be found using the following formula:
Px = (mx2 + nx1) / (m + n)
Py = (my2 + ny1) / (m + n)
In this case, P1(1, -4) and P2(4, 2) are the endpoints of the line segment, and the point we want to find divides the line externally in the ratio 1:4. This means that m = 1 and n = 4.
Now, let's substitute these values into the section formula:
Px = (1*4 + 4*1) / (1 + 4)
= (4 + 4) / 5
= 8 / 5
= 1.6
Py = (1*(-4) + 4*2) / (1 + 4)
= (-4 + 8) / 5
= 4 / 5
= 0.8
Therefore, the coordinates of the point that divides P1(1, -4) and P2(4, 2) externally in the ratio 1:4 are approximately (1.6, 0.8).
Since none of the given options match these coordinates, it seems that there might be an error in the answer choices. It is possible that the correct answer is not listed among the options provided.
The section formula states that if a line segment AB is divided by a point P in the ratio m:n, then the coordinates of P can be found using the following formula:
Px = (mx2 + nx1) / (m + n)
Py = (my2 + ny1) / (m + n)
In this case, P1(1, -4) and P2(4, 2) are the endpoints of the line segment, and the point we want to find divides the line externally in the ratio 1:4. This means that m = 1 and n = 4.
Now, let's substitute these values into the section formula:
Px = (1*4 + 4*1) / (1 + 4)
= (4 + 4) / 5
= 8 / 5
= 1.6
Py = (1*(-4) + 4*2) / (1 + 4)
= (-4 + 8) / 5
= 4 / 5
= 0.8
Therefore, the coordinates of the point that divides P1(1, -4) and P2(4, 2) externally in the ratio 1:4 are approximately (1.6, 0.8).
Since none of the given options match these coordinates, it seems that there might be an error in the answer choices. It is possible that the correct answer is not listed among the options provided.
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Find the coordinates of the point which divides P1(1, -4) and P2(4, 2) externally in the ratio 1 : 4.a)(0, -6)b)(6, -6)c)(0, -8)d)None of theseCorrect answer is option 'A'. Can you explain this answer?
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