The distance between the point (4, 3) and the intersection of y = 2x + 4 and y = 7 - x is

Assessment: JAMB UTME - Mathematics - 2012 Subject: General Mathematics

Question 1 Report

The distance between the point (4, 3) and the intersection of y = 2x + 4 and y = 7 - x is
Answer Details
The first step is to find the intersection point of the two lines y = 2x + 4 and y = 7 - x. To do this, we can set the two equations equal to each other and solve for x: 2x + 4 = 7 - x 3x = 3 x = 1 So, the intersection point is (1, 2). Next, we can use the distance formula to find the distance between the point (4, 3) and the intersection point (1, 2): distance = √((4 - 1)^2 + (3 - 2)^2) = √((3^2) + (1^2)) = √(9 + 1) = √10 = √(2 * 5) = √2 * √5 = 3√2. So, the distance between the two points is 3√2.

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