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Question
The midpoint of the points on x + y = 4, which are 4 units from 4x + 3y - 10 = 0 is the point of intersection of the two lines given.
The midpoint of the points on x + y = 4, which are 4 units from 4x + 3y - 10 = 0 is the point of intersection of the two lines given.
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Solution
The correct option is A True
We draw perpendicularfrom L2 to meet L1 at different points. Some of these perpendicular are going to be 1 unit. As we can see the length of the perpendicular is zero at the point of contact and it increases as we move on either side. We can see that there will be exactly two points which are at unit distance from L2. Let those points be P(x1,y1) and Q(x2,y2).
The two triangle formed are congruent triangles.
⇒ OP=OQ
⇒ O is the midpoint of P and Q. To find the midpoint, we just have to find the point of intersection.
True
We draw perpendicularfrom L2 to meet L1 at different points. Some of these perpendicular are going to be 1 unit. As we can see the length of the perpendicular is zero at the point of contact and it increases as we move on either side. We can see that there will be exactly two points which are at unit distance from L2. Let those points be P(x1,y1) and Q(x2,y2).
The two triangle formed are congruent triangles.
⇒ OP=OQ
⇒ O is the midpoint of P and Q. To find the midpoint, we just have to find the point of intersection.
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