Question

ABC is an isosceles right triangle in which AB has a slope of -1 and mABC = 90. ABC is dilated by a scale factor of 1.8 with the origin as the center of dilation, resulting in the image A'B'C'. What is the slope of B'C'?

Answer 1

Solution:

It is given that Δ ABC is an Isosceles right triangle right angled at B.

Slope of AB= -1

Also, AB ⊥ BC

⇒So,  Slope of AB  × Slope of BC = -1→→[If two lines are perpendicular then product of slopes of two lines is -1.]

⇒(-1) × Slope of BC = -1

⇒ Slope of BC = 1

Now, ABC is dilated by a scale factor of 1.8 with the origin as the center of dilation, resulting in the image A'B'C'.

→Length of Line segment A'B'= 1.8 × AB

So, slope of two line Segment that is AB and A'B' are same.

Slope of A'B'= -1

⇒Length of Line segment C'B'= 1.8 × CB

So, slope of two lines that is CB and C'B' are same.

⇒ Slope of B'C' = 1