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x_("mid ")=(x_(1)+x_(2))/(2)
The formula gives the
x-coordinate,
x_("mid "), of the midpoint of a line segment whose endpoints have
x-coordinates
x_(1) and
x_(2). Which of the following equations correctly gives the
x-coordinate of the second endpoint,
x_(2), in terms of the
x-coordinates of the first endpoint and of the midpoint?
Choose 1 answer:
(A)
x_(2)=2x_("mid ")-x_(1)
(B)
x_(2)=2x_("mid ")-(x_(1))/(2)
(C)
x_(2)=2x_("mid ")-2x_(1)
(D)
x_(2)=x_("mid ")-(x_(1))/(2)

$x_{\text {mid }}=\frac{x_{1}+x_{2}}{2}$ $\newline$ The formula gives the $x$ -coordinate, $x_{\text {mid }}$ , of the midpoint of a line segment whose endpoints have $x$ -coordinates $x_{1}$ and $x_{2}$ . Which of the following equations correctly gives the $x$ -coordinate of the second endpoint, $x_{2}$ , in terms of the $x$ -coordinates of the first endpoint and of the midpoint? $\newline$ Choose $1$ answer: $\newline$ (A) $x_{2}=2 x_{\text {mid }}-x_{1}$ $\newline$ (B) $x_{2}=2 x_{\text {mid }}-\frac{x_{1}}{2}$ $\newline$ (C) $x_{\text {mid }}$ $0$ $\newline$ (D) $x_{\text {mid }}$ $1$

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Find equations of tangent lines using limits

Full solution

Q.

x_{\text {mid }}=\frac{x_{1}+x_{2}}{2}

\newline

The formula gives the

x

-coordinate,

x_{\text {mid }}

, of the midpoint of a line segment whose endpoints have

x

-coordinates

x_{1}

and

x_{2}

. Which of the following equations correctly gives the

x

-coordinate of the second endpoint,

x_{2}

, in terms of the

x

-coordinates of the first endpoint and of the midpoint?

\newline

Choose

1

answer:

\newline

(A)

x_{2}=2 x_{\text {mid }}-x_{1}

\newline

(B)

x_{2}=2 x_{\text {mid }}-\frac{x_{1}}{2}

\newline

(C)

x_{\text {mid }}

0

\newline

(D)

x_{\text {mid }}

1

Midpoint formula: We start with the midpoint formula: $x_{\text{mid}}=\frac{x_{1}+x_{2}}{2}$
Multiply by $2$ : We need to solve for $x_{2}$ , so we multiply both sides by $2$ : $2\times x_{\text{mid}}=x_{1}+x_{2}$
Isolate $x_2$ : Next, we subtract $x_{1}$ from both sides to isolate $x_{2}$ : $x_{2}=2\cdot x_{\text{mid}}-x_{1}$

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