Find the condemned (y) if the distance between the points p(7,1) and Q (3,y) is 5

To find the value of y if the distance between the points P(7,1) and Q(3,y) is 5, you can use the distance formula: Distance = √((x2 - x1)^2 + (y2 - y1)^2) In this case, P(7,1) is (x1, y1) and Q(3,y) is (x2, y2). We want the distance to be 5: 5 = √((3 - 7)^2 + (y - 1)^2) Now, square both sides of the equation to eliminate the square root: 25 = (3 - 7)^2 + (y - 1)^2 25 = (-4)^2 + (y - 1)^2 25 = 16 + (y - 1)^2 Now, subtract 16 from both sides of the equation: 9 = (y - 1)^2 Take the square root of both sides (remembering that there are two possible solutions, one positive and one negative): y - 1 = ±√9 y - 1 = ±3 Now, solve for y in both cases: 1. y - 1 = 3 y = 3 + 1 y = 4 2. y - 1 = -3 y = -3 + 1 y = -2 So, there are two possible values for y: y = 4 and y = -2, depending on whether you take the positive or negative square root.