To determine the points on the
x-axis whose perpendicular distance from the line
‌+‌=1 is 4 units, we can use the formula for the perpendicular distance from a point
(x1,y1) to a line
Ax+By+C=0:Distance
=‌ First, let's rewrite the given line equation in the standard form:
‌+‌=1Multiplying through by 12 to clear the denominators, we get:
4x+3y−12=0 Now, we have the line equation in the standard form,
4x+3y−12=0. We need to find the points on the
x-axis that are 4 units away from this line. Points on the
x-axis have the form
(x1,0), so let's use the distance formula:
‌=4Simplifying this, we get:
‌=4 Multiplying both sides by 5 , we obtain:
|4x1−12|=20This leads to two cases:
Case 1:
4x1−12=20Solving for
x1 :
4x1=32⟹x1=8So, one point is
(8,0).
Case 2:
4x1−12=−20Solving for
x1 :
4x1=−8⟹x1=−2 So, the other point is
(−2,0).
Hence, the points on the
x-axis whose perpendicular distance from the line
‌+‌=1 is 4 units are
(8,0) and
(−2,0). Thus, the correct answer is:
Option A:
(8,0) and
(−2,0)