Question

The distance between the points (4,3) and (a,-2) is 5.Find the value of a.

Answer 1

Answer is in the attachment.

Answer 2

The correct answer is 4.

Given: Points =  (4,3) and (a,-2).

Distance between the points = 5.

To Find: The value of a.

Solution:

Distance between two points is calculated by distance formula.

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

Point 1 = (4, 3) and point 2 = (a, -2).

$\sqrt{(a-4 )^{2}+(-2-3 )^{2} }$ = 5

Square both the sides.

${(a-4 )^{2}+(-2-3 )^{2} }=25$

${(a-4 )^{2}+(-5)^{2} }=25$

${(a-4 )^{2}+25 }=25$

${(a-4 )^{2} }=0$

a - 4 = 0

a = 4

Hence, the value of a is 4.

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