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2 years ago

In the diagram, the areas of ADC and DCB are in a ratio of 3:4. what are the coordinates of point C

Mathematics

2 answers:

olchik [2.2K]2 years ago

8 0

the complete question in the attached figure

we know that

dAB=dAC+dCB

dAC=√((8-1)²+(-2+9)²)=√98

Area triangle ADC=dAC*CD/2

Area triangle DCB=dCB*CD/2

Area triangle ADC/Area triangle DCB=3/4

[dAC*CD/2]/[dCB*CD/2]=3/4

dAC=(3/4)*dCB-----------------------> equation (1)

dAB=dAC+dCB=√98

dAC=√98-dCB------------------------ > equation (2)

(1)=(2)

(3/4)*dCB=√98-dCB------------------> (7/4)*dCB=√98

dCB=(4/7)√98

dAC=√98-dCB-------- > √98-(4/7)√98-----à (3/7) )√98

dAC=(3/7) )√98

find the slope point A (1.-9) and point B (8,-2)

m=(-2+9)/(8-1)=7/7=1-------------- > 45°

dAC=(3/7)√98

the component x of dAC is

dACx=(3/7)√98*cos45°=(3/7)√98*√2/2=(3/7)√196=3

the component y of dAC is

dACy=dACx=3

the coordinates of the point C are

point A(1.-9)

Cx=Ax+dACx----------> 1+3=4

Cy=Ay+dACy----------> -9+3=-6

the coordinates C(4,-6)

the answer is C(4,-6)

ikadub [295]2 years ago

5 0

Answer:

C(4,-6) is correct on plato

Step-by-step explanation:

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2 years ago

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2 years ago

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Hi There!

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