Question

The line joining A(-3, 4) and B(2, -1) is parallel to the line joining C(1, -2) and D(0, x). Find x.​

Answer 1

The value of 'x' is equal to -1.

Given:

The line joining A (-3, 4) and B (2, -1) is parallel to the line joining C (1, -2) and D (0, x).

To Find:

The value of 'x'.

Solution:

→ The slope (m) of a line joining the points P (x₁ , y₁) and Q (x₂ , y₂) is given by the formula:

                               $\boldsymbol{Slope\:of\:the\:Line(m)=\frac{(y_{2} -y_{1} )}{(x_{2} -x_{1} )} }$

→ Calculating the slope of the line joining the points A (-3, 4) and B (2, -1):

                            $\boldsymbol{\because Slope\:of\:the\:Line=\frac{(y_{2} -y_{1} )}{(x_{2} -x_{1} )} }$

                  $\boldsymbol{\therefore Slope\:of\:the\:Line=\frac{-1-4 }{2-(-3 )}=\frac{-5 }{5}=-1 }$

   The slope of the line joining the points A (-3, 4) and B (2, -1) is -1.

→ Calculating the slope of the line joining the points C (1, -2) and D (0, x):

                             $\boldsymbol{\because Slope\:of\:the\:Line=\frac{(y_{2} -y_{1} )}{(x_{2} -x_{1} )} }$

                 $\boldsymbol{\therefore Slope\:of\:the\:Line=\frac{x-(-2) }{0-1}=\frac{x+2 }{-1}=(-x-2) }$

    The slope of the line joining the points C (1, -2) and D (0, x) is (-x - 2).

→ Since the line joining A (-3, 4) and B (2, -1) is parallel to the line joining C (1, -2) and D (0, x) , therefore their slopes must be equal.

                                           ∴ (-x - 2) = -1

                                           ∴ -(x) = -1 + 2

                                           ∴ -(x) = 1

                                           ∴ x = -1

Therefore the value of 'x' comes out to be equal to -1.

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Answer 2

Answer: The value of x is $-1$.

Given: The line joining A(-3, 4) and B(2, -1) is parallel to the line joining C(1, -2) and D(0, x).

To Find: The value of x.

Step-by-step explanation:

Step 1: If both lines are parallel to each other then their slope must be equal. And we know that the slope of a line passing to two points $(x_1,y_1)$ and $(x_2,y_2)$ is $\frac{(y_2-y_1)}{(x_2-x_1)}$.

Step 2: For first line $y_2=-1$, $y_1=4$ and $x_2=2$, $x_1=-3$ using this we can find out the slope of the line passing through these points.

The slope of first line $=\frac{(-1-4)}{(2-(-3))}$$=\frac{-5}{5}=-1$  ....eq(1)

Step 3: For second line $y_2=x$, $y_1=-2$ and $x_2=0$, $x_1=1$ using this we can find out the slope of the line passing through these points.

The slope of second line $=\frac{(x-(-2))}{(0-1)}$$=-(x+2)$ ...eq(2)

Step 4: As we know that the slope of the lines are equal, so from equation (1) and (2) we get,

$-1=-(x+2)$

$x=1 -2$

$x=-1$

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