If the distance between (3, a) and (4, 1) is | vedclass

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Question

(A) The distance between points $A(3, a)$ and $B(4, 1)$ is given by the distance formula: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.Given $d = \sqrt{

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(A) The distance between points $A(3, a)$ and $B(4, 1)$ is given by the distance formula: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.Given $d = \sqrt{10}$,we have $\sqrt{(4 - 3)^2 + (1 - a)^2} = \sqrt{10}$.Squaring both sides,we get $(4 - 3)^2 + (1 - a)^2 = 10$.$1^2 + (1 - 2a + a^2) = 10$.$1 + 1 - 2a + a^2 = 10$.$a^2 - 2a + 2 = 10$.$a^2 - 2a - 8 = 0$.Factoring the quadratic equation: $(a - 4)(a + 2) = 0$.Thus,$a = 4$ or $a = -2$.Since $4$ is provided in option $A$,the correct value is $4$.

If the distance between $(3, a)$ and $(4, 1)$ is $\sqrt{10},$ then the value of $a$ is $ \ldots \ldots \ldots \ldots .$

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