Distance formula:-
Distance between two points
1. (x_1, y_1)(x1,y1) &
2. (x_2, y_2)(x2,y2)
is given by sqrt((x_1-x_2)^2 + (y_1-y_2)^2)√(x1−x2)2+(y1−y2)2.
In this case,
distance = 13;
(x_1, y_1) = (-2, -5)(x1,y1)=(−2,−5);
(x_2, y_2) = (a, 7)(x2,y2)=(a,7);
therefore 13 = sqrt((-2-a)^2 + (-5-7)^2)
squaring both sides,
implies 13^2 = (a^2 + 4*a + 4) + 144
implies 169 = a^2 + 4*a + 148
implies a^2 + 4*a + 148 = 169
implies a^2 + 4*a -21 = 0 which is a quadratic equation
because solution of a quadratic equation of the form p*x^2 + q*x + r =0 ;
where p, q, r are constants is given by:-
x = (-q +- sqrt(q^2 - 4*p*r))/(2*)
in our case x becomes a and constants p, q, r become 1, 4, -21 respectively
therefore a = (-4 +- sqrt(4^2 - 4*(-21)*1))/(2*1)
implies a = (-4 +- sqrt100)/2
implies a=(-4 +- 10)/2
implies a = -14/2 , 6/2
implies a = -7 or 3
therefore a can be either -7 or 3.
