The reflection of the point (1,1) along the line y = -x is

Question

The reflection of the point (1,1) along the line y = -x is (A) (0,0) (B) (-1,1) (C) (-1,-1) (D) (1,-1)

Tardigrade Admin · Accepted Answer

The mid-point of PQ lies on x + y = 0 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/6dac64ea8eb9c76898880ceedc5251df-.png" /> ((h+1/2))+((k+1/2))=0 h+k=- 2 dots(i) Again, PQ is perpendicular to AB. ∴ ((k-1/h-1))(-1)=-1 (∵ m1 m2 = -1) ⇒ k-1=h-1 ⇒ k=h Put k = h in Eq. (i), we get 2h =-2 ⇒ h=-1 ∴ K=-1

Q. The reflection of the point $(1, 1)$ along the line $y = - x$ is

$(0, 0)$

$(- 1, 1)$

$(- 1, - 1)$

$(1, - 1)$

Q. The reflection of the point (1,1) along the line y=−x is

(0,0)

(−1,1)

(−1,−1)

(1,−1)

The mid-point of PQ lies on x+y=0 (2h+1​)+(2k+1​)=0 h+k=−2…(i) Again, PQ is perpendicular to AB. ∴(h−1k−1​)(−1)=−1(∵m1​m2​=−1) ⇒k−1=h−1 ⇒k=h Put k = h in Eq. (i), we get 2h=−2 ⇒h=−1 ∴K=−1

Q. The reflection of the point $(1, 1)$ along the line $y = - x$ is

$(0, 0)$

$(- 1, 1)$

$(- 1, - 1)$

$(1, - 1)$