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3 years ago

Midpoint (2,5) (-1,9)

Mathematics

1 answer:

Natasha_Volkova [10]3 years ago

4 0

The midpoint of the 2 points is (0.5, 7)

Hope this helps you

-AaronWiseIsBae

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2 years ago

Write the point-slope form of an equation of the line through the points (-7, 7) and (4, 1).

seraphim [82]

Answer:

Choice B. $\displaystyle y - 7 = -\frac{6}{11} \, (x + 7)$ .

Step-by-step explanation:

Start by finding the slope of this line. Let $(x_1,\, y_1)$ and $(x_2,\, y_2)$ represent two distinct points on a line on a Cartesian Plane. (That is, $x_1 \ne x_2$ .) The slope of this line would be:

$\displaystyle \frac{y_2 - y_1}{x_2 - x_1}$ .

For the line in this question:

$x_1 = -7$ ,
$y_1 = 7$ ;

$x_2 = 4,$
$y_2 = 1$ .

Indeed, $x_1 \ne x_2$ . The slope of this line would thus be $\displaystyle \frac{1 - 7}{4 - (-7)}$ , which is equal to $\displaystyle -\frac{6}{11}$ .

On a Cartesian Plane, the point-slope form of a line that has a slope of $m$ and includes the point $(x_0,\, y_0)$ can be written as:

$y - y_0 = m\, (x - x_0)$ .

(Note the minus signs in this form.)

For the line in this question, $m = \displaystyle -\frac{6}{11}$ . There are two equivalent expressions for its point-slope form:

Using the first point, $y - 7 = \displaystyle -\frac{6}{11}\, (x - (-7))$ . This equation is equivalent to $y - 7 = \displaystyle -\frac{6}{11}\, (x + 7)$ .
Using the second point, $y - 1 = \displaystyle -\frac{6}{11}\, (x - 4)$ .