Triangle ABC, a (5, - 2), B (7,3) are known, and the midpoint m of AC is on the Y axis, and the midpoint n of BC is on the X axis. Q: 1. The coordinates of vertex C; 2. The equation of line Mn | Math enthusiast | Mathematical art

Triangle ABC, a (5, - 2), B (7,3) are known, and the midpoint m of AC is on the Y axis, and the midpoint n of BC is on the X axis. Q: 1. The coordinates of vertex C; 2. The equation of line Mn

1. Let the coordinates (x, y) of C be 5 + x = 0 because the midpoint m of AC is on the Y axis,
X = - 5, and the midpoint n of BC is on the X axis, so y + 3 = 0, y = - 3
So C (- 5, - 3)
2. Because C (- 5, - 3), we get m (0, - 5 / 2), n (1,0) from the title
Let the equation of the line Mn be y = KX + B,
So - 5 / 2 = B, 0 = K + B, so k = 5 / 2, B = - 5 / 2
So the equation of the line Mn is y = 5 / 2x-5 / 2

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