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3 years ago

Find the other endpoint of the line segment with the given endpoint and midpoint. Endpoint: (-2, -6) Midpoint: (-5, 1)

Mathematics

1 answer:

FromTheMoon [43]3 years ago

3 0

Answer:

(-8,8)

Step-by-step explanation:

The midpoint $M(x_M,y_M)$ of the segment AB with endpoints $A(x_A,y_A)$ and $B(x_B,y_B)$ has coordinates

$x_M=\dfrac{x_A+x_B}{2}\\ \\y_M=\dfrac{y_A+y_B}{2}$

In your case, $A(-2,-6), \ M(-5,1),$ then

$-5=\dfrac{-2+x_B}{2}\Rightarrow -2+x_B=-10,\ x_B=-10+2=-8\\ \\1=\dfrac{-6+y_B}{2}\Rightarrow -6+y_B=2,\ y_B=2+6=8$

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Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm.

melamori03 [73]

Answer:

$6+2\sqrt{21}\:\mathrm{cm^2}\approx 15.17\:\mathrm{cm^2}$

Step-by-step explanation:

The quadrilateral ABCD consists of two triangles. By adding the area of the two triangles, we get the area of the entire quadrilateral.

Vertices A, B, and C form a right triangle with legs $AB=3$ , $BC=4$ , and $AC=5$ . The two legs, 3 and 4, represent the triangle's height and base, respectively.

The area of a triangle with base $b$ and height $h$ is given by $A=\frac{1}{2}bh$ . Therefore, the area of this right triangle is:

$A=\frac{1}{2}\cdot 3\cdot 4=\frac{1}{2}\cdot 12=6\:\mathrm{cm^2}$

The other triangle is a bit trickier. Triangle $\triangle ADC$ is an isosceles triangles with sides 5, 5, and 4. To find its area, we can use Heron's Formula, given by:

$A=\sqrt{s(s-a)(s-b)(s-c)}$ , where $a$ , $b$ , and $c$ are three sides of the triangle and $s$ is the semi-perimeter ( $s=\frac{a+b+c}{2}$ ).

The semi-perimeter, $s$ , is:

$s=\frac{5+5+4}{2}=\frac{14}{2}=7$

Therefore, the area of the isosceles triangle is:

$A=\sqrt{7(7-5)(7-5)(7-4)},\\A=\sqrt{7\cdot 2\cdot 2\cdot 3},\\A=\sqrt{84}, \\A=2\sqrt{21}\:\mathrm{cm^2}$

Thus, the area of the quadrilateral is:

$6\:\mathrm{cm^2}+2\sqrt{21}\:\mathrm{cm^2}=\boxed{6+2\sqrt{21}\:\mathrm{cm^2}}$

4 0

3 years ago

what is the equation of a line in slope intercept form that is perpendicular to y=2x+2 and passes through the point (8,-4)

miv72 [106K]

Answer:

The equation of the line that is perpendicular to y = 2x + 2 is

y = -1/2x

Step-by-step explanation:

The original equation is y = 2x + 2; it's slope is 2

Any line perpendicular to this equation would have to have a slope that is the negative reciprocal of the original slope.

Example:

y = 2x + 2 so,

the perpendicular line's slope must be -1/2

Write a new equation with the new slope:

y = -1/2x + b

We know that this line passes through (8, -4)

Plug these coordinates in the equation to find b, the y-intercept

-4 = -1/2 (8) + b

-4 = -4 + b

0 = b

b = 0

We do not have to write y = -1/2x + 0

So, our final answer is "y = -1/2x is perpendicular to y = 2x+2"

7 0

2 years ago

During a bite challenge rattlers how to collect various colored ribbons each 1/2 mile they collect a red ribbon each 1/8 mile th

tino4ka555 [31]

1/2×4=4/8
1/8=1/8
1/4×2=2/8
so 4/8+2/8=6/8
and 6/8+1/8=7/8

so 7/8 ribbons will be collected

7 0

3 years ago

Read 2 more answers

A student measured the dimensions of a table and recorded the length as 103.50cm and the width as 73.75cm. according to the stud

PolarNik [594]

The table is usually the shape of a rectangle. The area is equal to the length times the width. To make sure, let's recalculate the solution.

Area = length × width
Area = 103.50 cm × 73.75 cm
Area = 7,633.125 cm²

So, we established that the answer is correct. Now, I'll introduce the concept of significant figures. There are rules regarding significant figures to be applied conventionally in measurements and calculations. This is to increase precision of the data. Significant figures are digits that carry meaning. When you are given data with a specific number of significant figures, the final answer should also contain the same number of significant figures. In convention, the rule says that the zero's after non-zero digits after the decimal point are significant. Also, all non-zero digits are significant. The value 103.50 has 5 significant figures, and 73.75 has 4. When it comes to multiplication, the answer should contain the least significant figures. So, we should have 4 significant figures. Therefore, the final answer to be reported should be 7,633 cm².

8 0

3 years ago

A jacket with an original price of $67.80 is discounted 10%. What is the sale price?

Advocard [28]

I’m pretty sure it is $61.02

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3 years ago