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3 years ago

Find the coordinates of Rif M(-4, 5) is the midpoint of RS and S has coordinates (0, -10).

Mathematics

1 answer:

alexandr402 [8]3 years ago

3 0

Answer: R = (-8, 20)

Step-by-step explanation:

Given that :

M is the midpoint of RS

M = (-4, 5)

S = (0, - 10)

NOTE :

midpoint, M equals

Mx = (Rx + Sx) / 2

My = (Ry + Sy) / 2

Mx = - 4, Sx = 0, My = 5, Sy = - 10

Mx = (Rx + Sx) / 2

-4 = (Rx + 0) / 2

-8 = Rx + 0

Rx = - 8

My = (Ry + Sy) / 2

5 = (Ry + (-10)) / 2

10 = Ry - 10

10 + 10 = Ry

Ry = 20

Hence, coordinates of R = - 8 and 20

R = (-8, 20)

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Paragraph Proofs

charle [14.2K]

For the proof here kindly check the attachment.

We are given that $r\parallel s$ . Also, the transversal is shown. Let us take the first case, that of $\angle 1$ and $\angle 5$ . Please note that all other proofs will follow in a similar manner.

Let us begin, please have a nice look at the diagram. We will see that $\angle 1$ and $\angle 3$ are vertically opposite angles. We know that vertically opposite angles are congruent. Thus, $\angle 1$ and $\angle 3$ are congruent angles.

$\angle 1$ = $\angle 3$

Now, we know that $\angle 3$ and $\angle 5$ are alternate interior angles. We also, know that alternate interior angles are equal too. Thus, we have:

$\angle 3$ = $\angle 5$

From the above arguments it is clear that:

$\angle 1$ = $\angle 3$ = $\angle 3$ .

Thus, $\angle 1$ = $\angle 3$

We have proven the first instance. Please note that all other instances can be proved in a similar fashion.

For example, for $\angle 2$ and $\angle 6$ we can take $\angle 2$ and $\angle 4$ as vertically opposite angles thus making $\angle 2$ = $\angle 4$ . Now, $\angle 4$ and $\angle 6$ are alternate interior angles and thus $\angle 4$ and $\angle 6$ are equal. Thus, we have $\angle 2$ and $\angle 6$ .