enable us to think of the element on y axis equidistant from given factors is (0, y) then distance of (0, y) from element (7, -7) = distance of (0, y) from element (2, 2) [(0-7)^2 + (y+7)^2]^0.5 = [(0-2)^2 + (y-2)^2]^0.5 forty 9 + y^2 + 14y + forty 9 = 4 +y^2 -4y +4 18y = -ninety y = -5 subsequently the required element is (0, -5)
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Verified answer
point is on y-axis so x-coordinate value =0, so the point is (0, y)
find the distance between the point (0,y) and (1, –7) and (5, –1).
find the distance using the formula = sqrt((y2-y1)^2 + (x2-x1)^2)
the point is equidistant from the point (0,y). so, the equate the distance to two points
sqrt((y-(-7))^2+(0-1)^2 = sqrt((y-(-1))^2+(0-5)^2
(y-(-7))^2+(0-1)^2 = (y-(-1))^2+(0-5)^2
y^2 +14y + 49 +1 = y^2 + 2y + 1 +25
14y + 50 = 2y + 26
12y = 26 - 50
2y = -24
y = -2
point (0, -2)
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enable us to think of the element on y axis equidistant from given factors is (0, y) then distance of (0, y) from element (7, -7) = distance of (0, y) from element (2, 2) [(0-7)^2 + (y+7)^2]^0.5 = [(0-2)^2 + (y-2)^2]^0.5 forty 9 + y^2 + 14y + forty 9 = 4 +y^2 -4y +4 18y = -ninety y = -5 subsequently the required element is (0, -5)