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The line which is passing through points (-1, 4) and (2, 6) is perpendicular to the line through the points (3, 7) and (x, 8). Find the value of x.

The line which is passing through points (-1, 4) and (2, 6) is perpendicular to the line through the points (3, 7) and (x, 8). Find the value of x. Correct Answer <span class="math-tex">\(\frac{7}{3}\)</span>

Given:

One line : (-1,4) and (2,6)

Other line : (3,7) and (x,8)

Formula:

When two lines are perpendicular then product of their slope is -1.

Slope of line passing through (x1,y1) and (x2,y2) = (y2 - y1)/(x2 - x1)

Calculation:

Slope of line passing through (-1,4) and (2,6) = (6 - 4)/(2 - (-1)) = 2/3

Slope of line passing through (3,7) and (x,8) = (8 - 7)/(x - 3) = 1/(x - 3)

Then,

⇒ 2/3 × 1/(x - 3) = -1

⇒ 2 = -3x + 9

⇒ -3x  = -7

∴ x = 7/3

 

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