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Which of the ...

Question

Which of the following represents the equation of line segment joining $z_{1} = - 3 + 4 i$ and $z_{2} = 7 - 4 i .$

A

| z + 3 - 4 i | - | z - 7 + 4 i | = 10

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B

| z - 3 - 4 i | + | z - 7 + 4 i | = | - 10 + 8 i |

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C

| z - 3 - 4 i | + | z - 7 + 4 i | = 4

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D

| z + 3 - 4 i | - | z - 7 + 4 i | = | - 10 + 8 i |

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Solution

The correct option is D $| z + 3 - 4 i | - | z - 7 + 4 i | = | - 10 + 8 i |$
The equation of line segment joining $z_{1}$ and $z_{2}$ is given by $| z - z_{1} | + | z - z_{2} | = | z_{1} - z_{2} |$
Putting in the values we get:
$| z - (- 3 + 4 i) | - | z - (7 - 4 i) | = | (- 3 + 4 i) - (7 - 4 i) |$
$| z + 3 - 4 i | - | z - 7 + 4 i | = | - 10 + 8 i |$

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Similar questions

z_{1} = 3 + 4 i

z_{2} = - 3 - 4 i

then the equation

| z - z_{1} | + | z - z_{2} | = 10

Q. Which of the following represents the equation of the line segment joining

z_{1} = 3 i

z_{2} = 3 \sqrt{3} .

| Z_{1} - 3 - 4 i | = 2

| Z_{2} - 3 - 4 i | = 5

, then the maximum distance between the

Z_{1}

Z_{2}

| Z_{1} - 3 - 4 i | = 2

| Z_{2} - 3 - 4 i | = 5

, then the minimum distance between the

Z_{1}

Z_{2}

z_{1} = 1 + 2 i, z_{2} = 2 + 3 i, z_{3} = 3 + 4 i,

z_{1}, z_{2}

z_{3}

represent the vertices of

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