Practice set 1( mathamatics) Important for jee mains exam
Answers
EXPLANATION.
Image of the point (-8,12)
The line mirror 4x + 7y + 13 = 0.
As we know that,
Slope of the perpendicular line = b/a.
Slope of the line 4x + 7y + 13 = 0 is 7/4.
Formula of :
Equation of the line.
⇒ (y - y₁) = m(x - x₁).
Put the values in the equation, we get.
⇒ (y - 12) = 7/4(x - (-8)).
⇒ (y - 12) = 7/4(x + 8).
⇒ 4(y - 12) = 7(x + 8).
⇒ 4y - 48 = 7x + 56.
⇒ 7x + 56 - 4y + 48 = 0.
⇒ 7x - 4y + 104 = 0.
Solving both the equation, we get.
⇒ 4x + 7y + 13 = 0. - - - - - (1).
⇒ 7x - 4y + 104 = 0. - - - - - (2).
Multiply equation (1) by 4.
Multiply equation (2) by 7.
⇒ 4x + 7y + 13 = 0. - - - - - (1). x 4.
⇒ 7x - 4y + 104 = 0. - - - - - (2). x 7.
We get,
⇒ 16x + 28y + 52 = 0. - - - - - (3).
⇒ 49x - 28y + 728 = 0. - - - - - (4).
Adding equation (3) & (4), we get.
⇒ 65x + 780 = 0.
⇒ 65x = - 780.
⇒ x = - 780/65.
⇒ x = - 12.
Put the value of x = - 12 in the equation (1), we get.
⇒ 4x + 7y + 13 = 0.
⇒ 4(-12) + 7y + 13 = 0.
⇒ - 48 + 7y + 13 = 0.
⇒ 7y - 35 = 0.
⇒ 7y = 35.
⇒ y = 5.
Values of x = - 12 and y = 5.
Their Co-ordinates = (-12,5).
Point O is the mid-point of the line.
Mid-point formula = (a + b)/2.
⇒ (α - 8)/2 = - 12.
⇒ α - 8 = - 24.
⇒ α = - 16.
⇒ (β + 12)/2 = 5.
⇒ β + 12 = 10.
⇒ β = - 2.
The Co-ordinates = (-16,-2).
Option [D] is correct answer.
Answer:
(d) is the correct answer.
