1. L(15. 1) is the midpoint of the straight line joining point (p. - 2) to point D(-1. q) find p and q.2. M is the midpoint of the straight line joining point A (3. 1/5) to point B.If m has coordinates (7. 3), find the coordinates of B.
Accepted Solution
A:
1. The values of p and q are: p=31 and q= 42. B(11, 29/5)Further explanation:1. L(15. 1) is the midpoint of the straight line joining point (p. - 2) to point D(-1. q) find p and q.Given:M = (15. 1)(x1, y1) = (p, -2)(x2, y2) = (-1, q)The formula for mid-point is:[tex](\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2}) = M \\Putting\ the\ values\\(\frac{p-1}{2} , \frac{-2+q}{2}) = (15,1)\\Putting\ realtive\ values\ equal\\\frac{p-1}{2} = 15\\p-1 = 15(2)\\p-1 = 30\\p = 30+1\\p = 31\\\frac{-2+q}{2} =1\\-2+q = 2(1) \\-2+q = 2\\q = 2+2 \\q =4[/tex]Hence,p=31q=42. M is the midpoint of the straight line joining point A (3. 1/5) to point B.If m has coordinates (7. 3), find the coordinates of B.Here, (x1,y1) = (3, 1/5)(x2, y2) = ?M(x,y) = (7,3)Putting values in the formula of mid-point[tex](\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2}) = M\\(\frac{3+x_2}{2} , \frac{1/5+y_2}{2}) = (7,3)\\\frac{3+x_2}{2} = 7\\3+x_2 = 7*2\\3+x_2 = 14\\x_2 = 14-3\\x_2 = 11\\\frac{\frac{1}{5}+y_2}{2} = 3\\{\frac{1}{5}+y_2} = 3*2\\{\frac{1}{5}+y_2} = 6\\y_2 = 6 - \frac{1}{5}\\y_2 = \frac{30-1}{5}\\y_2 = \frac{29}{5}[/tex]So, the coordinates of point B are (11, 29/5) .Keywords: Finding mid-point, Finding coordinates through mid-pointLearn more about coordinate geometry at:brainly.com/question/7437053brainly.com/question/9087716#LearnwithBrainly