The coordinates of point T are (14,20). The midpoint of ST Is (7,-8). Find the coordinates of point S

Mathematics

1 answer:

BARSIC [14]1 year ago

5 0

The coordinate of point S will be ( 0, -36).

<h3>What are coordinates?</h3>

A pair of numbers used to express the location of a point on a coordinate plane using the horizontal and vertical distinctions from the two reference axes. usually represented by pairs of x-values and y-values (x,y).

Coordinates are always written in the form of small brackets the first term will be x and the second term will be y.

Let say the coordinate of S is (x , y)

Given that

(7,-8) is midpoint the of ST

So,

(x + 14)/2 = 7

x = 0

And

(y + 20)/2 = -8

y = -36

Hence coordinate of point S will be ( 0, -36).

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Show tan(???? − ????) = tan(????)−tan(????) / 1+tan(????) tan(????)<br> .

anyanavicka [17]

Answer:

See the proof below

Step-by-step explanation:

For this case we need to proof the following identity:

$tan(x-y) = \frac{tan(x) -tan(y)}{1+ tan(x) tan(y)}$

We need to begin with the definition of tangent:

$tan (x) =\frac{sin(x)}{cos(x)}$

So we can replace into our formula and we got:

$tan(x-y) = \frac{sin(x-y)}{cos(x-y)}$ (1)

We have the following identities useful for this case:

$sin(a-b) = sin(a) cos(b) - sin(b) cos(a)$

$cos(a-b) = cos(a) cos(b) + sin (a) sin(b)$

If we apply the identities into our equation (1) we got:

$tan(x-y) = \frac{sin(x) cos(y) - sin(y) cos(x)}{sin(x) sin(y) + cos(x) cos(y)}$ (2)

Now we can divide the numerator and denominato from expression (2) by $\frac{1}{cos(x) cos(y)}$ and we got this:

$tan(x-y) = \frac{\frac{sin(x) cos(y)}{cos(x) cos(y)} - \frac{sin(y) cos(x)}{cos(x) cos(y)}}{\frac{sin(x) sin(y)}{cos(x) cos(y)} +\frac{cos(x) cos(y)}{cos(x) cos(y)}}$