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Dahasolnce [82]
2 years ago
15

What are the coordinates of point B in the diagram?

Mathematics
2 answers:
Andrej [43]2 years ago
8 0
Let the cordinates of B be (x, y), then
(3(1) + x)/4 = 1.75 and (3(5) + y)/4 = 2.5
3 + x = 7 and 15 + y = 10
x = 7 - 3 and y = 10 - 15
x = 4 and y = -5

Therefore, the coordinate of B is (4, -5)
Vinil7 [7]2 years ago
6 0

Answer:  The co-ordinates of point B are (4, -5).

Step-by-step explanation:  We are given to find the co-ordinates of point B in the diagram.

From the diagram, we note that

the co-ordinates of point A and C are (1, 5) and (1.75, 2.5) respectively.

Also, the point C divides the line segment AB internally in the ratio 1 : 3.

We know that if a point P divides a line segment joining the points (a, b) and (c, d) internally in the ratio m : n, then the co-ordinates of the point P are

P=\left(\dfrac{mc+na}{m+n},\dfrac{md+nb}{m+n}\right).

Here, (a, b) = (1, 5), m : n = 1 : 3  and  (c, d) = ?

Therefore, the co-ordinates of point C will be

C=\left(\dfrac{1\times c+3\times1}{1+3},\dfrac{1\times d+3\times5}{1+3}\right)\\\\\\\Rightarrow (1.75,2.5)=\left(\dfrac{c+3}{4},\dfrac{d+15}{4}\right)\\\\\\\Rightarrow 1.75=\dfrac{c+3}{4},~~~~~2.5=\dfrac{d+15}{4}\\\\\\\Rightarrow c+3=7,~~~~~~~~\Rightarrow d+15=10\\\\\\\Rightarrow c=4,~~~~~~~~~~~~~\Rightarrow d=-5.

Thus, the co-ordinates of point B are (4, -5).

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Find the Measure of B<br><br>Topic: Inscribed Angles and Central Angles
Oxana [17]

Answer:

Option B

The measure of angle b is 75°

Step-by-step explanation:

Method 1

we know that

In a inscribed quadrilateral, the opposite angles are supplementary

so

∠a+60°=180° ------> equation A

∠b+105°=180° -----> equation B

To find the measure of angle b solve the equation B

∠b+105°=180°

Subtract 105° both sides

∠b+105°-105°=180°-105°

∠b=75°

Method 2

see the attached figure with letters to better understand the problem

we know that

The inscribed angle measures half that of the arc comprising

so

∠105°=(1/2)[arc ADC]

arc ADC=2*105°=210°

<em><u>Find the measure of arc ABC</u></em>

we know that

arc ABC+arc ADC=360° -----> by complete circle

arc ABC=360°-210°=150°

<u><em>Find the measure of inscribed angle b</em></u>

∠b=(1/2)[arc ABC]

substitute

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