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Vsevolod [243]
2 years ago
11

Point A has coordinates (6,4) and point B has coordinates (2,7) write AB as column vector. Plz plz plz

Mathematics
1 answer:
Olenka [21]2 years ago
7 0

Answer:

\overrightarrow{AB }=\begin{bmatrix}-4\\3 \end{bmatrix}

Step-by-step explanation:

<u>Column Vector</u>

Vectors are matrices having only one column or one row. A vector having only one column is called a column vector, and a vector having only one row is called a row vector.

It's required to find the vector AB as a column vector, and we are given the coordinates of A=(6,4) and B=(2,7).

The vector directed from A to B is found by subtracting its corresponding coordinates:

\overrightarrow{AB }=

\overrightarrow{AB }=

Now we express the vector as a one-column matrix as follows:

\overrightarrow{AB }=\begin{bmatrix}-4\\3 \end{bmatrix}

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Step-by-step explanation:

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In the two Δ KDE and KCD:

∵ m∠KDE = m∠KCD

∵ m∠DKE = m∠CKD

∵ DK is a common side

∴ Δ KDE is similar to ΔKCD

∴ \frac{KD}{KC}=\frac{DE}{CD}=\frac{KE}{KD}

∵ DE : CD = 5 : 3

∴ \frac{KD}{KC}=\frac{5}{3}

∴ KD = 5/3 KC

∵ KE = KC + 8

∵ \frac{KE}{KD}=\frac{5}{3}

∴ \frac{KC+8}{\frac{5}{3}KC }=\frac{5}{3}

∴ KC + 8 = \frac{25}{9}KC

∴ \frac{25}{9}KC - KC=8

∴ \frac{16}{9}KC=8

∴ KC = (8 × 9) ÷ 16 = 4.5

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(if you don’t know what I’m doing here is that I’m removing the negative 5 by putting a positive 5 since both of them make 0. Also the “x” always stay alone and the unit stays as the unit)

(I putted the positive under the 0 because what u do to the unit you need to do the same thing with the other.)

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