The line through the points (– 2, 6) and (4, 8) is perpendicular to

1.	The line through the points (– 2, 6) and (4, 8) is perpendicular to the line through the points (8, 12) and (x, 24). Find the value of x.
Answer» To Find: Find the value of x ? The concept used: If two line is perpendicular then, the product of their slopes is – 1. Explanation: We have two lines having point A(– 2,6) and B(4,8) and other line having points C(8,12) and D(x,24). The formula used: The slope of the line, m = \(\frac{y_2-y_1}{x_2-x_1}\) Now, The slope of Line AB is, m_AB = \(\frac{4-(-2)}{8-6}\) m_AB = \(\frac{6}{2}\) and, The slope of Line CD is, m_CD = \(\frac{x-8}{24-12}\) m_CD = \(\frac{x-8}{12}\) We know the product of the slopes of perpendicular line is always – 1. Then, m_AB x m_CD = – 1 \(\frac{6}{2}\times\frac{x-8}{12}\) = -1 \(\frac{x-8}{12}\) = -1 x – 8 = – 4 x = – 4 + 8 x = 4 Hence, The value of x is 4.

The line through the points (– 2, 6) and (4, 8) is perpendicular to the line through the points (8, 12) and (x, 24). Find the value of x.

Answer»

To Find: Find the value of x ?

The concept used: If two line is perpendicular then, the product of their slopes is – 1.

Explanation: We have two lines having point A(– 2,6) and B(4,8) and other line having points C(8,12) and D(x,24).

The formula used: The slope of the line, m = \(\frac{y_2-y_1}{x_2-x_1}\)

Now, The slope of Line AB is, m_AB = \(\frac{4-(-2)}{8-6}\)

m_AB = \(\frac{6}{2}\)

and, The slope of Line CD is, m_CD = \(\frac{x-8}{24-12}\)

m_CD = \(\frac{x-8}{12}\)

We know the product of the slopes of perpendicular line is always – 1.

Then, m_AB x m_CD = – 1

\(\frac{6}{2}\times\frac{x-8}{12}\) = -1

\(\frac{x-8}{12}\) = -1

x – 8 = – 4

x = – 4 + 8

x = 4

Hence, The value of x is 4.