The dimensions of a triangle are shown below. if the height of the triangle is increased by the factor of 4, which statement will be true about the area of the triangle?

a. the area will increase by a factor of 2.
b. the area will increase by a factor of 4.
c. the area will increase by a factor of 8
d. the area will not change

Option B. The area will increase by a factor of 4

Step-by-step explanation:

we know that

The area of triangle is equal to

where

b is the base of triangle

h is the height of triangle

If the height of the triangle is increased by the factor of 4

then

The new area of the triangle will be

The new area is 4 times the original area

therefore

The area will increase by a factor of 4

one way is to plot 2 points and connect them which is what the answer choices seem to be doing

it seems to be using the y intercept and the slope

y=mx+b, m=slope, b=y-intercept (where the line hits the y axis)

slope=rise/run

y-intercept is where the line croses the y axis which is the y value where x=0

you seem to have given the wrong slope (you didn't put a number in front of te x, it should be 2/3 or 3/2 looking at the answer options)

y=? x-1

m=? because of your fault

b=-1

so it has a slope of ? and y intercept of -1, meaning it pases through (0,-1)

so draw point (0,-1) (so answer is one of the first 2 option)

if slope is 2/3, then go up 2 and right 3 then draw line through those 2 points

if slope is 3/2, then go up 3 and right 2 then draw line through those 2 points