The point A(4,-6) is reflected over the point (-1,-5) and its image is point B. What ar coordinates of point B? Answer

To find the coordinates of point B, we need to reflect point A over point (-1,-5).<br /><br />Step 1: Find the midpoint between point A and point (-1,-5).<br />The midpoint formula is given by:<br />Midpoint = ((x1 + x2)/2, (y1 + y2)/2)<br /><br />Using the midpoint formula, we can find the midpoint between point A and point (-1,-5):<br />Midpoint = ((4 + (-1))/2, (-6 + (-5))/2)<br />Midpoint = (3/2, -11/2)<br /><br />Step 2: Reflect point A over the midpoint.<br />To reflect a point over a midpoint, we need to find the distance between the point and the midpoint, and then move the same distance on the other side of the midpoint.<br /><br />Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)<br />Distance = sqrt((4 - (-1))^2 + ((-6) - (-5))^2)<br />Distance = sqrt(5^2 + (-1)^2)<br />Distance = sqrt(25 + 1)<br />Distance = sqrt(26)<br /><br />Since we are reflecting point A over the midpoint, we need to move the same distance on the other side of the midpoint. Therefore, the coordinates of point B will be:<br />B = (Midpoint_x - Distance, Midpoint_y - Distance)<br />B = (3/2 - sqrt(26)/2, -11/2 - sqrt(26)/2)<br /><br />Therefore, the coordinates of point B are (3/2 - sqrt(26)/2, -11/2 - sqrt(26)/2).