Mathematics: Select the correct answer.in the diagram, the areas of triangle abc and triangle dce are in a ratio of 3 : 4. what are the coordinates of point c? a. (3, -7)b. (5, -5)c. (7, -3)d. (4, -6)

70%Step-by-step explanation:14 divided by 2014/20=0.714/20 x 100 to calculate the percentage which is 70% because 70/100 will also give 0.7(7/10) so similar...

Select the correct answer.in the diagram, the areas

Ответ:

irishdreamer0689

05.01.2022

Mathematics

The correct option is (D) (4, -6).

Step-by-step explanation: Given that the areas of the triangles ADC and DCB are in the ratio 3 : 4.

We are to find the co-ordinates of point C.

From the diagram, we note that

the co-ordinates of point A and B are A(1, -9) and B(8,-2).

So, the length of the line segment AB, calculated by distance formula, is

$AB=\sqrt{(1-8)^2+(-9+2)^2}=\sqrt{49+49}=7\sqrt2.$

Now, area of ΔADC is

$A_{ABC}=\dfrac{1}{2}\times AC\times CD,$

and area of ΔDCB is

$A_{DCE}=\dfrac{1}{2}\times BC\times CD.$

According to the given information, we have

$A_{ADC}:A_{DCB}=3:4\\\\\\\Rightarrow \dfrac{A_{ADC}}{A_{DCE}}=\dfrac{3}{4}\\\\\\\Rightarrow \dfrac{\frac{1}{2}\times AC\times CD}{\frac{1}{2}\times BC\times CD}=\dfrac{3}{4}\\\\\\\Rightarrow \dfrac{AC}{BC}=3:4.$

So, the point C divides the line segment AB internally in the ratio 3 : 4.

We know that

if a point divides a line segment with end-points (a, b) and (c, d) internally in the ration m : n, then its co-ordinates are

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

Since point C divides the line segment AB with end-points A(1, -9) and B(8, -2) internally, so the co-ordinates of point C will be

$\left(\dfrac{3\times 8+4\times 1}{3+4},\dfrac{3\times (-2)+4\times (-9)}{3+4}\right)\\\\\\=\left(\dfrac{28}{7},\dfrac{-42}{7}\right)\\\\\\=(4, -6).$

Thus, the co-ordinates of point C are (4, -6).

Option (D) is correct.

0,0(0 оценок)

Select the correct answer.

in the diagram, the areas of triangle abc and triangle dce are in a ratio of 3 : 4. what are the coordinates of point c?

a.
(3, -7)
b.
(5, -5)
c.
(7, -3)
d.
(4, -6)

Ответ:

Ответ:

Ask your question to the AI advisor

More tips

Answers on questions: Mathematics

Ask an AI advisor a question