Question

In the question, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice.
Assertion: The value of 𝒚 is 3. for which the distance between the points 𝑷(𝟐, –𝟑) and 𝑸(𝟏𝟎, 𝒚) is 10.
Reason: Distance between two given points 𝑨(𝒙𝟏, 𝒚𝟏) 𝑎𝑛𝑑 𝑩(𝒙𝟐, 𝒚𝟐) is given by $\sqrt{(}{x}_2-x_1{)}^2+(y_2-y_1{)}^2$.

Answer 1

Distance formula D = $\sqrt{(}{x}_2-x_1{)}^2+(y_2-y_1{)}^2$
The value of 𝒚 is 3. for which the distance between the points 𝑷(𝟐, –𝟑) and 𝑸(𝟏𝟎, 𝒚) is 10 (Given in the assertion)
Apply the distance formula-
10 = $\sqrt{(}10-2{)}^2+(y-(-3){)}^2$
10 = $\sqrt{(}64+(y+3){)}^2$
Squaring both the side we get
$100=64+9+y^2+6y$
$y^2+6y-27=0$
$y^2+9y-3y-27=0$
$y(y+9)-3(y+9)=0$
$(y+9)(y-3)=0$
y = 3, -9 >
Hence we can say that both assertion and reason are true and and reason is the correct explanation of assertion.