M (c, -1) is a point equidistant from the points A(1, 3) and B(-5, -5). Find the value of c.
-2
Given
∵ Distance between points (x1,y1) and(x2,y2) is √(x2−x1)2+(y2−y1)2.
∴ AM = √(c−1)2+(−1−3)2 and BM = √(c−(−5))2(−1−(−5))2
∵ Distance AM = Distance BM
∴√(c−1)2+(−1−3)2=√(c−(−5))2(−1−(−5))2⇒√(c−1)2+16=√(c+5)2+16⇒(c−1)2+16=(c+5)2+16⇒−2c+17=10c+41⇒12c=−24⇒c=−2
∴ Point M is (−2,−1).