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3 years ago

Collinear points are two or more points that lie on the same

Mathematics

1 answer:

muminat3 years ago

7 0

Answer: Line

Explanation: Points that lie on the same line are called <em>collinear</em> points.

I'll show you an example.

Below, points E, B, and D are collinear since they lie on the same line.

I have highlighted the line green to see it more clearly.

However, C, B, and D would not be collinear

since they don't all lie on the same line.

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The coordinates of midpoint M and endpoint Q of a segment are M(–7, 8) and Q(–19, 30). Find the coordinates of the other endpoin

Margaret [11]

Answer:

Step-by-step explanation:

Use the midpoint formula to solve:

$M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

We know the midpoint and one set of coordinates, so filling those in:

$(-7,8)=(\frac{x+(-19)}{2},\frac{y+30}{2})$

Since the -7 is the x coordinate of the midpoint, we set the x part of the equation equal to -7 and solve for x, and then do the same for y. The 2 equations are:

$-7=\frac{x-19}{2}$ and $8=\frac{y+30}{2}$ We solve each one of these to get the x and y coordinates of the other endpoint. In both cases, multiply both sides of the equations by 2 and then solve by either adding or subtracting.

-14 = x - 19 so

5 = x

16 = y + 30 so

-14 = y

The coordinates of the other endpoint are (5, -14)

4 0

2 years ago

The figure shows the layout of a symmetrical pool in a water park. What is the area of this pool rounded to the tens place? Use

k0ka [10]

Answer:

$2489ft^{2}$

Step-by-step explanation:

The pool are is divided into 4 separated shapes: 2 circular sections and 2 isosceles triangles. Basically, to calculate the whole area, we need to find the area of each section. Due to its symmetry, both triangles are equal, and both circular sections are also the same, so it would be enough to calculate 1 circular section and 1 triangle, then multiply it by 2.

<h3>Area of each triangle:</h3>

From the figure, we know that <em>b = 20ft </em>and <em>h = 25ft. </em>So, the area would be:

$A_{t}=\frac{b.h}{2}=\frac{(20ft)(25ft)}{2}=250ft^{2}$

<h3>Area of each circular section:</h3>

From the figure, we know that $\alpha =2.21 radians$ and the radius is $R=30ft$ . So, the are would be calculated with this formula:

$A_{cs}=\frac{\pi R^{2}\alpha}{360\°}$

Replacing all values:

$A_{cs}=\frac{(3.14)(30ft)^{2}(2.21radians)}{6.28radians}$

Remember that $360\°=6.28radians$

Therefore, $A_{cs}=994.5ft^{2}$

Now, the total are of the figure is:

$A_{total}=2A_{t}+2A{cs}=2(250ft^{2} )+2(994.5ft^{2})\\A_{total}=500ft^{2} + 1989ft^{2}=2489ft^{2}$

Therefore the area of the symmetrical pool is $2489ft^{2}$

3 0

3 years ago

Building a is 190 feet shorter than building

MaRussiya [10]

We will solve this using a system of equations. The first part tells us that building a is 190 feet shorter than building b. Our first equation, then, is b=190+a. The second part tells us that the addition of the two buildings' heights is 1480. So our second equation is a + b = 1480. The first equation is already solved for b, so let's sub that value into the second equation for b: a+(190+a)=1480. 2a + 190 = 1480 and 2a = 1290. That means that building a is 645 feet tall. Building b is 190 feet taller, so b = 190 + 645, which is 835.

3 0

3 years ago

Determine the difference between the monthly payments on a $120,000 home at 6.5% and at 8% for 15 years

slega [8]

Answer:

I believe the answer is 1800

Step-by-step explanation:

120000 * 0.065 = 7800

120000 * 0.08 = 9600

9600 - 7800 = 1800

3 0

3 years ago

A and B are two similar shapes the area of shape A is 200cm2 calculate the area of shape B

barxatty [35]

Answer:

Area of shape B = 312.5 cm²

Step-by-step explanation:

Ratio of Area of A : Area of B = 12² : 15²

Given that area of A is 200 cm², let the area of shape B = x

Therefore:

200:x = 12²:15²

200/x = 144/225

Cross multiply

144x = 200*225

144x = 45,000

x = 45,000/144

x = 312.5 cm²

Area of shape B = 312.5 cm²

5 0

2 years ago