Question

2) Use a graph to find the length of DE if D(4, -3) and E(-5, -7) in pythagoras theorem.

Answer 1

Use a graph to find the length of DE if D(4, -3) and E(-5, -7) in pythagoras theorem.​

we know that

Applying the Pythagorean Theorem

DE^2=DEx^2+DEy^2

DEx -----> is the distance in the x-coordinate

DEy -----> is the distance in the y-coordinate

DEx=(-5-4)=-9 ------> subtract the x-coordinates

DEy=(-7+3)=-4 -----> subtract the y-coordinates

substitute in the formula

DE^2=(-9)^2+(-4)^2

DE^2=97

`DE=\sqrt[]{97}\text{ units}`

c^2=a^2+b^2

c -----> is the distance DE

a ----> horizontal leg

b ----> vertical leg

we have

a=(-5-4)=-9 ------> subtract the x-coordinates

b=(-7+3)=-4 -----> subtract the y-coordinates

substitute

c^2=(-9)^2+(-4)^2

c^2=97

`c=\sqrt[]{97}\text{ units}`