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Virty [35]
3 years ago
8

Q # 18 Find the midpoint of. A B

Mathematics
1 answer:
Lady_Fox [76]3 years ago
4 0
Point A lies on the x-axis and distance from point A to the y-axis is 2 units, then the coordinates of A are (-2,0) (-2, because A lies on the left side from the origin and 0 because A lies on x-axis).
The distances from point B to the x-axis and y-axis are 2 and 4, then tha coordinates of point B are (4,2).
To find the middle-point M of segment AB you should use formulas: x_M= \dfrac{x_A+x_B}{2}  \\ y_M= \dfrac{y_A+y_B}{2}.
Then x_M= \dfrac{-2+4}{2}=1 \\ y_M= \dfrac{0+2}{2}=1.
Answer: M(1,1), correct choice is C.

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D)) The ratio of the monthly income and expenditure of Sunayana is 5 : 3. If she
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Answer:

Sunayana's income is ₹25000 and expenditures are ₹15000.

Step-by-step explanation:

Let i denote the monthly income and e denote the expenditures.

We know that the ratio of the monthly income to expenditure is 5:3. So, we can write the following proportion:  

\frac{i}{e}=\frac{5}{3}

Let's multiply both sides by e. This yields:

i=\frac{5}{3}e

We know that when the income is <em>increased</em> by 5000 and the expenditures are <em>decreased </em>by 3000, the new ratio is 5:2. So, we can write the following proportion:

\frac{i+5000}{e-3000}=\frac{5}{2}

Let's multiply both sides by (e-3000):

i+5000=\frac{5}{2}(e-3000)

Since we know that i=\frac{5}{3}e, substitute:

\frac{5}{3}e+5000=\frac{5}{2}(e-3000)

So, let's solve for the expenditures. Distribute the right:

\frac{5}{3}e+5000=\frac{5}{2}e-7500

Subtract \frac{5}{2}e from both sides:

-\frac{5}{6}e+5000=-7500

Subtract 5000 from both sides:

-\frac{5}{6}e=-12500

Multiply both sides by -6/5. So, the expenditures are:

e=\text{Rs }15000

We can use the original ratio to find Sunayana's income:

i=\frac{5}{3}e

Substitute 15000 for e. Evaluate:

i=\frac{5}{3}(15000)=\text{Rs }25000

So, Sunayana's income is ₹25000 and expenditures are ₹15000.

And we're done!

Edit: Wrong currency, sorry about that!

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