Subjects geometry

Rectangle Coordinates 86680C

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1. Problem 14 to 30 includes multiple distinct questions, but per instructions, we solve only the first one, which is 25.a: Find the coordinates of M and draw the rectangle. 2. Given points for triangle JKLM: J(-1,1), K(4,2), L(0,2), M(0,0). 3. To find M for the rectangle formed by points J, K, L, and M, we check if these points form a rectangle and find M accordingly. 4. A rectangle has opposite sides equal and parallel. Given J, K, and L, we find M such that JKLM is a rectangle. 5. Vector JK = K - J = (4 - (-1), 2 - 1) = (5, 1). 6. Vector JL = L - J = (0 - (-1), 2 - 1) = (1, 1). 7. For rectangle, vector JM = vector JK + vector JL = (5,1) + (1,1) = (6,2). 8. Coordinates of M = J + vector JM = (-1,1) + (6,2) = (5,3). 9. So, M = (5,3). 10. The rectangle vertices are J(-1,1), K(4,2), L(0,2), M(5,3). 11. To draw the rectangle, plot these points and connect them in order J-K-M-L-J. Final answer: Coordinates of M are (5,3).