Find the distance of the pt (2,3) from the line 2x - 3y +
9 = 0 measured along a line making an angle of 45°
with X-axis.
Answers
the distance of the point (2,3) from the line 2x - 3y + 9 = 0 measured along a line making an angle 45° with x-axis is 4√2 unit
we have to find the distance of point (2,3) from the line 2x - 3y + 9 = 0 measured along a line making an angle 45° with x-axis .
we know, slope of line is tangent of angle made by line with positive direction of x-axis.
so, slope of line = tan45° = 1
now equation of line passing through (2,3) and slope 1 is given as,
(y - 3) = 1(x - 2)
⇒y = x - 2 + 3 = x + 1
⇒y = x + 1
now find the point of intersection of line y = x + 1 and 2x - 3y + 9 = 0
2x - 3(x + 1) + 9 = 0
⇒2x - 3x - 3 + 9 = 0
⇒-x + 6 = 0
⇒ x = 6 and y = x + 1 = 7
so, point of intersection of lines is (6,7)
now we have to find the distance between (6,7) and (2,3).
distance (6,7) and (2,3) = √(6 - 2)² + (7 - 3)²} = 4√2 unit
hence, required distance is 4√2 unit
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