Question

Given B(17,5), C(11, -3), D(-1, 2), and
E(x, -6), find the value of .r so that BC||DE.

Answer 1

To find the value of ( x ) so that ( BC ) is parallel to ( DE ), we need to ensure that the slopes of the two lines are equal. Therefore, calculate the slope of line segment ( BC ) and line segment ( DE ) using their respective endpoints, then set them equal to each other and solve for ( x ).

Step-by-step explanation:

The slope ( m ) of a line passing through two points
`\( (x_1, y_1) \) and \( (x_2, y_2) \)` is given by the formula:

`\[ m = (y_2 - y_1)/(x_2 - x_1) \]`

For line segment ( BC ), with points
`\( B(17,5) \) and \( C(11, -3) \), the slope (\( m_(BC) \)) is:`

`\[ m_(BC) = (-3 - 5)/(11 - 17) = (-8)/(-6) = (4)/(3) \]`

For line segment ( DE ), with points ( D(-1, 2) ) and ( E(x, -6) ), the slope
`(\( m_(DE) \))` is calculated in terms of ( x ):

`\[ m_(DE) = ((-6 - 2))/((x - (-1))) = (-8)/((x + 1)) \]`

Since ( BC ) is parallel to ( DE ), their slopes must be equal:

`\[ (4)/(3) = (-8)/((x + 1)) \]`

Cross-multiply and solve for ( x ):

[ 4(x + 1) = -24 ]

[ 4x + 4 = -24 ]

[ 4x = -28 ]

[ x = -7 ]

Therefore, the value of ( x ) is -7 to make ( BC ) parallel to ( DE ).