To find the distance between (-2,-3) and (4,1), peggy's teacher drew a diagram and marked blue lines to represent the legs of a right triangle. peggy then used 42 and 62 to find the distance represented by the red segment. what distance did she find ?

The distance between  (-2,-3) and (4,1) is units

The distance between two points and is given by the formula:

For the points (-2, -3) and (4, 1):

x₁ = -2,  y₁  =  -3,  x₂ = 4 y₂ = 1

Substitute x₁ = -2,  y₁  =  -3,  x₂ = 4 y₂ = 1 into the formula above:

The distance between  (-2,-3) and (4,1) is units

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Step-by-step explanation:

we know that

the formula to calculate the distance between two points is equal to

in this problem we have

substitute the values

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .