The vertices of a triangle are A(0,0),B(3,8) and C(9,0). What is the area of this triangle?

Mathematics

1 answer:

Svetradugi [14.3K]2 years ago

5 0

Answer:

Step-by-step explanation:

To find the area of a triangle where you know the x and y coordinates of the three vertices, you'll need to use the coordinate geometry formula: area = the absolute value of Ax(By - Cy) + Bx(Cy - Ay) + Cx(Ay - By) divided by 2. Ax and Ay are the x and y coordinates for the vertex of A. The same applies for the x and y notations of the B and C vertices.

Fill in the numbers for each corresponding letter combination within the formula.

Fill in your formula like this: 0(8-10) + 3(0-0) + 9(0-8).

Subtract the numbers within the parentheses.

0 from 8 = 8, 0 from 0 = 0 and 8 from 10 = 2.

Multiply that result by the number to the left of the parentheses.

0 by 8 = 0, 3 by 0 = 0 and 9 by 2 = 18.

Add the three products together.

0 + 0 + 18 = 18

Divide the sum of the three products by 2.

18 ÷ 2 = 9

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. Mrs. Rojas deposited $8000 into an account paying 4% interest annually. After 8 months Mrs. Rojas withdrew the $6000 plus inte

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well, keeping in mind that a year has 12 months, that means that 8 months is 8/12 of a year, when Mrs Rojas pull her money out.

$~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$6000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\to \frac{8}{12}\dotfill &\frac{2}{3} \end{cases} \\\\\\ A=6000[1+(0.04)(\frac{2}{3})]\implies A=6000\left( \frac{77}{75} \right)\implies A=6160$

well, she put in 6000 bucks, got back 160 extra, that's the interest earned in the 8 months.

what if she had left her money for 1 whole year, then

$~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$6000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ t=years\dotfill &1 \end{cases} \\\\\\ A=6000[1+(0.04)(1)]\implies A=6240$

so had she left it in for a year, she'd have gotten 6240, namely 240 in interest, well, what fraction of a year's interest was earned? or worded differently, what fraction is 160(8 months) of 240(1 year)?

$\cfrac{\stackrel{\textit{for 8 months}}{160}}{\underset{\textit{for 12 months}}{240}}\implies \cfrac{2}{3}$