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The formula for the distance between two points (x_1, y_1) and (x_2, y_2) is given by: d = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2) a) Find the length of the line joining (1,2) and (4,6). Step 1: Identify the coordinates. Let (x_1, y_1) = (1,2) and (x_2, y_2) = (4,6). Step 2: Substitute the coordinates into the distance formula. d = sqrt((4 - 1)^2 + (6 - 2)^2) Step 3: Simplify the expression. d = sqrt((3)^2 + (4)^2) d = sqrt(9 + 16) d = sqrt(25) d = 5 b) Find the length of the line joining (-1,4) and (2,6). Step 1: Identify the coordinates. Let (x_1, y_1) = (-1,4) and (x_2, y_2) = (2,6). Step 2: Substitute the coordinates into the distance formula. d = sqrt((2 - (-1))^2 + (6 - 4)^2) Step 3: Simplify the expression. d = sqrt((2 + 1)^2 + (2)^2) d = sqrt((3)^2 + (2)^2) d = sqrt(9 + 4) d = sqrt(13) c) Find the length of the line joining (-1,-4) and (3,-2). Step 1: Identify the coordinates. Let (x_1, y_1) = (-1,-4) and (x_2, y_2) = (3,-2). Step 2: Substitute the coordinates into the distance formula. d = sqrt((3 - (-1))^2 + (-2 - (-4))^2) Step 3: Simplify the expression. d = sqrt((3 + 1)^2 + (-2 + 4)^2) d = sqrt((4)^2 + (2)^2) d = sqrt(16 + 4) d = sqrt(20) Step 4: Simplify the radical. d = sqrt(4 × 5) d = 2sqrt(5) Send me the next one 📸