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denis-greek [22]
3 years ago
15

Given the points C(-1,-5) and D(-7,11) find the coordinates of point E on CD such that the ratio of CE to ED is 5:3.

Mathematics
1 answer:
Anon25 [30]3 years ago
6 0

Answer:

The coordinates of point E on CD are \left(-\frac{19}{4},5 \right).

Step-by-step explanation:

Let be C = (-1,-5), D = (-7,11) and \frac{CE}{ED} = \frac{5}{3}. The given ratio can be translated vectorially into this:

\overrightarrow {CE} = \frac{5}{3} \cdot \overrightarrow{ED}

And let consider that each point is a vector with respect to origin:

\vec C = (-1, -5) and \vec {D} = (-7,11)

Then,

\vec E -\vec C = \frac{5}{3}\cdot (\vec D -\vec E)

\vec E +\frac{5}{3}\cdot \vec E = \frac{5}{3}\cdot \vec D + \vec C

\frac{8}{3}\cdot \vec E = \frac{5}{3}\cdot \vec D + \vec C

\vec E = \frac{5}{8}\cdot \vec D + \frac{3}{8}\cdot \vec C

\vec E = \frac{5}{8}\cdot (-7,11)+\frac{3}{8}\cdot (-1,-5)

\vec E = \left(-\frac{35}{8},\frac{55}{8}  \right)+\left(-\frac{3}{8},-\frac{15}{8}  \right)

\vec E = \left(-\frac{35}{8}-\frac{3}{8},\frac{55}{8}-\frac{15}{8}    \right)

\vec{E} = \left(-\frac{19}{4}, 5\right)

The coordinates of point E on CD are \left(-\frac{19}{4},5 \right).

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