A(0,a) is equidistant from P(3,-3) and Q(-2,2). Find a.

a = - 1

Step-by-step explanation:

Given the points are equidistant from A then AP = AQ

Calculate the distance using the distance formula

d =

with (x₁, y₁ ) = A(0, a) and (x₂, y₂ ) = P(3, - 3)

AP = = =

Repeat with (x₁, y₁ ) = A(0, a) and (x₂, y₂ ) = Q(- 2, 2)

AQ = = =

Equating AP and AQ

= ( square both sides )

9 + (- 3 - a)² = 4 + (2 - a )² ← expand parenthesis on both sides

9 + 9 + 6a + a² = 4 + 4 - 4a + a² ( subtract a² - 4a from both sides )

18 + 10a = 8 ( subtract 18 from both sides )

10a = - 10 ( divide both sides by 10 )

a = - 1

step-by-step explanation:

the areas of two similar triangles are 18 cm2 and 8 cm2. one of the sides of the first triangle is 4.5 cm. what is the length of the corresponding side of the other triangle?

what is the information provided?

step-by-step explanation: