Question

Find ‘a’ if the distance of the point (4, 1) from the point (3, a) is √10.

Answer 1

Answer:

a = -2 or a = 4

Step-by-step explanation:

Distance Formula between 2 points A = (x1,y1) and B = (x2,y2) is

AB = $\sqrt{(x_{1} - x_{2} )^{2} +(y_{1} - y_{2} )^{2} }$

AB is given as $\sqrt{10}$

x1 = 4, x2 = 3, y1 = 1 and y2 = a

Therefore $\sqrt{10}$ = $\sqrt{(4- 3 )^{2} +(1 - a )^{2} }$

Squaring and solving 10 = 1 + $(1 - a)^{2}$

$(1 - a)^{2}$ = 9

Taking square root of both sides

1 - a = 3 or 1 - a = -3

a = -2 or a = 4

Answer 2

Answer:

a=4

Step-by-step explanation:

point 1 is at (4,1)

point 2 is at (3,a)

pythagorean theorem

a^2+b^2 = c^2

a=(4-3), b=(a-1), c=√10

(4-3)^2 + (a-1)^2 c=10

1+(a-1)^2=10

(a-1)^2=9,

(a-1)(a-1)=9

a^2-2a+1=9

a^2-2a-8=0

(a+2)(a-4)=0

so, a=4, take the positive sign. hope this helps.