<div id="app">
  <transition name="card" mode="out-in">
    <div class="card" v-if="front == true" key="front">
      <h2>Sign In</h2>
      <div class="form">
        <h1>Sign In Form</h1>
      </div>
      <div class="footer">
        <span>Not a member?</span>
        <button @click="front = false">
          Join Us
        </button>
      </div>
    </div>
    <div class="card" v-else key="back">
      <h2>Sign Up</h2>
      <div class="form">
        <h1>Sign Up Form</h1>
      </div>
      <div class="footer">
        <span>Already a member?</span>
        <button @click="front = true">
          Log In
        </button>
      </div>
    </div>
  </transition>
</div>

#app {
  display: flex;
  justify-content: center;
}

.card {
  width: 300px;
  height: 210px;
  background-color: orange;
  text-align: center;
}

h1, h2 {
  color: white;
}

h2 {
  background-color: blue;
  margin-top: 0;
}

.form {
  width: 270px;
  height: 120px;
  background-color: green;
  margin: auto;
  display: flex;
  justify-content: center;
  align-items: center;
}

.footer {
  margin-top: 10px;
  margin-right: 15px;
  text-align: right;
}

.card-enter,
.card-leave-to {
  opacity: 0;
  transform: rotateY(90deg);
}

.card-enter-active,
.card-leave-active {
  transition: all 0.5s;
}

new Vue({
  el: '#app',
  data: {
    front: true
  }
})