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Basile [38]
3 years ago
10

What are the coordinates of the point LaTeX: \frac{3}{4}\:3 4of the way from A to B? coordinate plane with line segment AB. Poin

t A is at -5, -4 and point b at -3, 3
Mathematics
1 answer:
egoroff_w [7]3 years ago
6 0

Answer: \left(\dfrac{-7}{2},\dfrac{5}{4}\right).

Step-by-step explanation:

It is given that Point A is at (-5, -4) and point B at (-3, 3).

We need to find the coordinates of the point which is 3/4 of the way from A to B.

Let the required point be P.

AP:AB=3:4

AP:PB=AP:(AB-AP)=3:(4-1)=3:1

It means, point P divides segment AB in 3:1.

Section formula:  If a point divides a line segment in m:n, then

\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)

Using section formula, we get

P=\left(\dfrac{3(-3)+1(-5)}{3+1},\dfrac{3(3)+1(-4)}{3+1}\right)

P=\left(\dfrac{-9-5}{4},\dfrac{9-4}{4}\right)

P=\left(\dfrac{-14}{4},\dfrac{5}{4}\right)

P=\left(\dfrac{-7}{2},\dfrac{5}{4}\right)

Therefore, the required point is \left(\dfrac{-7}{2},\dfrac{5}{4}\right).

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Answer:

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Answer:

The height of the larger traffic signs is 51.96 inches

Step-by-step explanation:

Given that initially, A company makes traffic signs of an equilateral triangle with the perimeter of 144 inches

Now, A company makes similar traffic signs of perimeter 1.25 of original

New perimeter will be 1.25x144=180 inches

Let triangle ABC be a larger triangle with 180inches of the perimeter.

It is given that the triangle is an equilateral triangle,

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Figure show that triangle ABC and AD is the height of the triangle.

Since, the triangle ABC is an equilateral triangle,

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4(2p+3)=16<br> solve the equation
Natali5045456 [20]

Final Answer: p = \frac{1}{2}

Steps/Reasons/Explanation:

Question: Solve the equation 4(2p + 3) = 16.

<u>Step 1</u>: Divide both sides by 4.

2p + 3 = \frac{16}{4}

<u>Step 2</u>: Simplify \frac{16}{4} to 4.

2p + 3 = 4

<u>Step 3</u>: Subtract 3 from both sides.

2p = 4 - 3

<u>Step 4</u>: Simplify 4 - 3 to 1.

2p = 1

<u>Step 5</u>: Divide both sides by 2.

p = \frac{1}{2}

~I hope I helped you :)~

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