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Find the co-ordinates of the foot of the perpendiculardrawn from the point (2, 3) on the line 3x + 4y + 8 = 0 |
Answer» EXPLANATION.Co-ordinates of the FOOT of the perpendicular drawn from the point = (2,3). on the line = 3x + 4y + 8 = 0. As we know that, SLOPE of the perpendicular line = b/a. Slope of line : 3x + 4y + 8 = 0 is 4/3. Slope = 4/3. Equation of line, ⇒ (y - y₁) = m(X - x₁). Put the values in the equation, we get. ⇒ (y - 3) = 4/3(x - 2). ⇒ 3(y - 3) = 4(x - 2). ⇒ 3y - 9 = 4x - 8. ⇒ 3y - 4x - 9 + 8 = 0. ⇒ 3y - 4x - 1 = 0. As we know that, ⇒ 3x + 4y + 8 = 0. ⇒ (1). ⇒ 3y - 4x - 1 = 0. ⇒ (2). Solving equation (1) & (2), we get. Multiply equation (1) by 4 & (2) by 3, we get. ⇒ 12x + 16y + 32 = 0. ⇒ 9Y - 12x - 3 = 0. ⇒ 25y + 29 = 0. ⇒ y = -29/25. Put the value of y = -29/25 in equation (1), we get. ⇒ 3x + 4y + 8 = 0. ⇒ 3x + 4(-29/25) + 8 = 0. ⇒ 3x - 116/25 + 8 = 0. ⇒ 75x - 116 + 200 = 0. ⇒ 75x + 84 = 0. ⇒ 75 = -84. ⇒ x = -28/25. Their Co-ordinates = (-28/25, -29/25). |
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