All categories

1 year ago

Find the midpoint M of the line segment joining the points S = (-5, -3) and T = (7, 1). T

Mathematics

1 answer:

hichkok12 [17]1 year ago

8 0

Answer:

In geometry, the midpoint is the middle point of a line.

If two point (starting point and end point) is given

(x1 , y1) and (x2 , y2)

then their midpoint will be

(x,y) = { (x1+x2)/2 , (y1+y2)/2 }

so the midpoint M of the line segment joining the points S = (-5, -3) and T = (7, 1) will be

{(-5+7) / 2 , (-3+1)/2} = (1,-1) , is the midpoint of this line

Know more about “geometry” here: brainly.com/question/28367211

#SPJ9

You might be interested in

Find the equation of the sphere if one of its diameters has endpoints (4, 2, -9) and (6, 6, -3) which has been normalized so tha

Pavel [41]

Answer:

$(x - 5)^2 + (y - 4)^2 + (z - 6)^2 = 14$ .

(Expand to obtain an equivalent expression for the sphere: $x^2 - 10\,x + y^2 - 8\, y + z^2 - 12\, z + 63 = 0$ )

Step-by-step explanation:

Apply the Pythagorean Theorem to find the distance between these two endpoints:

$\begin{aligned}&\text{Distance}\cr &= \sqrt{\left(x_2 - x_1\right)^2 + \left(y_2 - y_1\right)^2 + \left(z_2 - z_1\right)^2} \cr &= \sqrt{(6 - 4)^2 + (6 - 2)^2 + ((-3) - (-9))^2 \cr &= \sqrt{56}}\end{aligned}$ .

Since the two endpoints form a diameter of the sphere, the distance between them would be equal to the diameter of the sphere. The radius of a sphere is one-half of its diameter. In this case, that would be equal to:

$\begin{aligned} r &= \frac{1}{2} \, \sqrt{56} \cr &= \sqrt{\left(\frac{1}{2}\right)^2 \times 56} \cr &= \sqrt{\frac{1}{4} \times 56} \cr &= \sqrt{14} \end{aligned}$ .

In a sphere, the midpoint of every diameter would be the center of the sphere. Each component of the midpoint of a segment (such as the diameter in this question) is equal to the arithmetic mean of that component of the two endpoints. In other words, the midpoint of a segment between $\left(x_1, \, y_1, \, z_1\right)$ and $\left(x_2, \, y_2, \, z_2\right)$ would be:

$\displaystyle \left(\frac{x_1 + x_2}{2},\, \frac{y_1 + y_2}{2}, \, \frac{z_1 + z_2}{2}\right)$ .

In this case, the midpoint of the diameter, which is the same as the center of the sphere, would be at:

$\begin{aligned}&\left(\frac{x_1 + x_2}{2},\, \frac{y_1 + y_2}{2}, \, \frac{z_1 + z_2}{2}\right) \cr &= \left(\frac{4 + 6}{2},\, \frac{2 + 6}{2}, \, \frac{(-9) + (-3)}{2}\right) \cr &= (5,\, 4\, -6)\end{aligned}$ .

The equation for a sphere of radius $r$ and center $\left(x_0,\, y_0,\, z_0\right)$ would be:

$\left(x - x_0\right)^2 + \left(y - y_0\right)^2 + \left(z - z_0\right)^2 = r^2$ .

In this case, the equation would be:

$\left(x - 5\right)^2 + \left(y - 4\right)^2 + \left(z - (-6)\right)^2 = \left(\sqrt{56}\right)^2$ .

Simplify to obtain:

$\left(x - 5\right)^2 + \left(y - 4\right)^2 + \left(z + 6\right)^2 = 56$ .

Expand the squares and simplify to obtain:

$x^2 - 10\,x + y^2 - 8\, y + z^2 - 12\, z + 63 = 0$ .

8 0

2 years ago

Put the numbers in order from least to greatest.

loris [4]

Answer:

B. -.9,-4, 1, .2, .8

Hope this helps!:)

7 0

2 years ago

Read 2 more answers

Which line best represents the line of best fit for this scatter plot? (5 points)

Bogdan [553]

Line Q, you always want the line that has as many dots on it as possible!! :)

7 0

2 years ago

An apple orchard sells apples in bags of 10.the orchard sold a total of 2,430 apples one day.how many bags of apples waa

Kruka [31]

243 bags of apples were sold in one day

6 0

3 years ago

Which absolute value function defines this graph?

iogann1982 [59]

If you describe the graph as a V with its vertex point on (0,0), then you are either describing the graph of y = |x| or y = 3|x|. The only difference is that the coordinates of y=3|x| is multiplied thrice the coordinates of y=|x|. In other words, this graph is thrice wider than the y=|x|.

Furthermore, y = -3|x| is a downward V, and
x = |y| and x = 3|y| looks like a V rotated side-ward,

5 0

3 years ago