2 point with a each name the point H and I
Answer (1)
Answer:The correctly identified points are H(3, 4) and I(3, 2).Step-by-step explanation:The question asks for a step-by-step explanation to find the coordinates of two points, H and I, that are 3 units from the y-axis and \sqrt{5} units from the point (5, 3). Step 1: Understand the problem We need to find two points, H and I. Both points must be 3 units away from the y-axis. This means their x-coordinates will be either 3 or -3. Additionally, both points must be \sqrt{5} units away from the point (5, 3). We'll use the distance formula to find the y-coordinates. Step 2: Use the distance formula The distance formula between two points (x_1, y_1) and (x_2, y_2) is \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}. We know the distance between our points (H and I) and (5,3) is \sqrt{5}. Step 3: Solve for points with x = 3 Let's first consider the case where the x-coordinate is 3. Plugging this into the distance formula: \sqrt{(5 - 3)^2 + (y - 3)^2} = \sqrt{5} Simplify and solve for y: $ (2)^2 + (y - 3)^2 = 5$$ 4 + (y - 3)^2 = 5$$ (y - 3)^2 = 1$$ y - 3 = ±1$$ y = 4$ or y = 2 This gives us two points: H(3, 4) and I(3, 2). Step 4: Solve for points with x = -3 Now let's consider the case where the x-coordinate is -3: \sqrt{(5 - (-3))^2 + (y - 3)^2} = \sqrt{5} Simplify and solve for y: $ (8)^2 + (y - 3)^2 = 5$$ 64 + (y - 3)^2 = 5$$ (y - 3)^2 = -59$ Since we can't have a negative number under a square root (we'd get an imaginary number), there are no solutions for this case. Step 5: State the solution Therefore, the coordinates of the two points are H(3, 4) and I(3, 2).
